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.
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
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
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
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.