The document summarizes the design and fabrication of a 3-axis CNC precision router. The objectives were to efficiently design and fabricate a router with micron-level precision at an economical cost for small industries in Pakistan. Various analyses including mathematical modeling, FEMA, static and dynamic analyses were performed to optimize the design. A 16mm ball screw diameter was justified. The router was fabricated using A36 steel with bolts, nuts, and pins. NEMA 23 motors, drivers, and infrared sensors were integrated along with Raspberry Pi and C# software. The router can accommodate multiple 3D printing heads and has future potential for milling and improved precision.

1. Design and Fabrication of
CNC Precision Router
Group 3
M. Ismail Leghari 2013248
M. Shoaib Butt 2013261
Saad Ali 2013318
Sarmad Ishfaq 2013338
Advisor
Prof. Dr. Wasim Ahmed Khan

2. Background
Expensive Technology
- Novel Technology In Pakistan
Import Restriction/Local Development
- Need has to catered locally for small industries
Accuracy and Precision
- Demand is increasing rapidly

3. Objectives
Efficiently design and fabricate a 3-Axis CNC router
with micron (10-6) level precision.
Incorporate multiple heads per customer demand.
-For numerous additive manufacturing processes
Most economical CNC precision router for small scale
industries of Pakistan.

4. Design Part

5. Initial Design

6. Final Design

7. Exploded View

8. Mechanical Specifications
• Fixed Gantry
• Moving Table
• Bed area = 250mm * 250mm
• ASTM A36 Steel used for the structure
• Machine Weight = 106 Kg
• Box Volume = 25cm * 25cm * 10cm
• Can accommodate multiple 3D Printing Heads

9. Material Parameters for Ball Screw
 Material AISI 6150 alloy steel
 Density 7850 kg/m3
 Modulus of Elasticity 200 GPa
 Poisson Ratio 0.3
 Yield Strength 415 MPa

10. Mathematical Model (To Find Max Beam Deflection Under Action of Load)
Assumption
• The ball screw behaves like a simply supported beam.
• Cross section area the beam is circular.
• As bed has extended size and there is some load over the bed. Uniformly
distributed load of 1180 N/m is applied from 0.2m to 0.3m as shown.
• Moment of magnitude 6.4 N.m is also applied at the center of beam at 0.25 m.

11. Analytical Solution
The following equations were developed to find the maximum displacement
of shaft.
𝑦1 =
1
E
∗
243.85𝑥3−39.77𝑥
d4 for 0 < x < 0.2m
𝑦2 =
1
E
∗
−1001.68𝑥4+1045.075𝑥3−240.388𝑥2−7.72346𝑥−1.6025
d4 for 0.2m < x < 0.25m
𝑦3 =
1
E
∗
−1001.68𝑥4+1045.075𝑥3−305.5775𝑥2−24.86945𝑥−5.67637
d4 for 0.25 < x < 0.3m
𝑦4 =
1
E
∗
−156.86𝑥3+235.295𝑥2−83.2988𝑥−2.43672
d4 for 0.3 < x < 0.4m

12. ABAQUS Solution (FEM)

13. Comparison of Analytical And Computation
Techniques
Major
Diameter
(mm)
Lead
(mm)
Max Deflection
Analytically (mm)
Max Deflection using
ABAQUS (mm)
% Difference
12 4 1.48 1.493 0.878378378
16 4 0.42 0.4128 1.714285714
20 4 0.19 0.194 2.105263158
25 4 0.078 0.0796 2.051282051
32 4 0.029 0.0293 1.034482759
40 5 0.0122 0.01223 0.245901639
50 10 0.0051 0.005046 1.058823529
• Less than 2.1 % difference in calculations from both techniques
• Confirms our methods

14. Torque and Critical Speed Calculations
• Torque
𝑇 =
𝐹.𝑑𝑚
2
𝑙+𝜋𝑓𝑑𝑚
𝜋𝑑𝑚−𝑓𝑙
+
𝐹.𝑓𝑐.𝑑𝑐
2
• Single threaded so lead ‘l’ will be equal to the pitch of screw
• Friction coefficient ‘f’, generally the material used for power screws is steel for
the screw and the nut is made of bronze. Value is between 0.10-0.15.

15. λ is a factor determined by the ball-screw support method where:
One end fixed and the other free, λ = 0.59π
Both ends simply supported, λ = π
One end fixed and the other simply supported, λ = 1.25π
Both ends fixed, λ = 1.49π
• Critical Speed
𝑛 𝑐𝑟 =
𝜆2
𝐿2
𝐸∗𝐼∗𝑔
𝛾∗𝐴
∗
60
2𝜋

16. Results of Torque and Critical Speed
Major Diameter
(mm)
Lead (mm) Torque ncr (rpm)
12 4 0.289968099 5702.357764
16 4 0.37384134 7603.143686
20 4 0.457938052 9503.929607
25 4 0.563193885 11879.91201
32 4 0.710668627 15206.28737
40 5 0.888335784 19007.85921
50 10 1.144845129 23759.82402

17. Static Analysis of the Ball Screw in Solidworks
• Mathematical model in FEM
software ABAQUS.
• 3D model is to be checked for
deflection in real conditions.
• Boundary conditions and forces
applied are shown in Figure .
• Gravity is also taken into
account to make the analysis
more realistic.
• Maximum deflection due to
static loading to be 0.28 mm

18. Dynamic Analysis of the Ball Screw in
Solidworks
• Working Parameter and Condition
mm/s rpm rad/s Hz
20 19.1 2 0.32
60 57.3 6 0.95
• To ensure that the natural frequency of the structure does not
resonates with the operating frequency

19. • Natural Modes of Frequency (First 5)
Frequency Number Rad/sec Hertz Seconds
1 1188.5 189.16 0.0052865
2 1192.4 189.77 0.0052695
3 3478.2 553.57 0.0018064
4 3490.9 555.6 0.0017999
5 6929.8 1102.9 0.00090669
Structure operating frequencies (0.32-0.95 Hz) in not within natural
frequency range.

20. Critical Node Response
• Most Critical node is
analyzed for the
maximum
displacement under
working conditions
• Results
• Max Displacement =
0.19 mm
• Frequency = 0.35 Hz

21. Justification of Dimension through different
analysis
• Mathematical model analysis = 0.42 mm
• Static Analysis = 0.28 mm
• Dynamic Analysis = 0.20 mm
 Can safely say that our structure is safe from vibrations
 Ball Screw Dimension = 16 mm

22. Fabrication Part

23. Assembly and Detailed BoQ

24. Fabrication Details
• Material Used
- A36 ( 415 MPa Yield )
• Joining Mechanism
- Square Plates
- Bolts and Nuts
- Pins (Push Fitting)
• Bearings Used
- External Flange
(Universal Ball Bearings)
• Noise Reduction Mechanism
-Ribs and Fins

25. 3D Printing Heads

26. Electronics and Software Parts

27. Electronics
• NEMA 23 motors
• 1.26 Nm Holding Torque
• 2 Phase
• 1.8 degree step angle
• 3A
• TB-6560 stepper motor drivers
• Sharp infrared sensors: range 2cm-15cm

28. Software
• Raspberry pi
• C sharp Language
• GUI
• I/O configuration
• Compatible with electronics

29. Future Prospects
• Material removal processes like vertical milling can also be performed
on the precision router after few minor modifications.
• Precision can be further enhanced to less than 2 microns by the
utilization of micro-stepping.