Abrasive Cut-Off MachineReport and the Detail Design of the Cut-Off Machine

MOW 217

Benade DJ 26317088

Kraamwinkel FH 26209382

Van Staden HJ 26059802

Table of Content

List of Tables......................................................................................................................................3

List of Figures.....................................................................................................................................4

List of Symbols...................................................................................................................................5

1. Introduction...................................................................................................................................6

2. User Requirements........................................................................................................................7

3. Literature Study.............................................................................................................................7

4. Functional Analysis........................................................................................................................8

4.1 System Level............................................................................................................................8

4.2 Mission Level...........................................................................................................................8

4.3 System Level Functional Diagram............................................................................................9

4.4 First Level Functional Diagram.................................................................................................9

4.5 Design Parameters per Function............................................................................................10

5. Design Specifications...................................................................................................................11

6. Concepts & Concept Evaluation...................................................................................................12

7. Design calculations......................................................................................................................15

7.1 Power Transmission and Torque............................................................................................15

7.2 Forces on Pulley.....................................................................................................................16

7.3 Shear Force and Bending Moment........................................................................................16

7.4 Safety Factor of Shaft (Dynamic)............................................................................................18

7.5 Safety Factor of Shaft (Fatigue)..............................................................................................19

7.6 Bearing Calculations...............................................................................................................20

7.7 Pulley Design..........................................................................................................................22

8. Detail Design................................................................................................................................22

List of Tables

List of Figures

Figure 5.1 Schematic Drawing for the cut-off machine layout.............................................................12Figure 5.2 Forces on cutting disc and pulley........................................................................................12

List of Symbols

Symbol UnitAngular Velocity ω rad/sAxial load Fa NBasic life rating L10 106 cyclesBending moment at Q MQ NmBending moment at R MR NmDiameter d d mmDiameter D D mmDynamic load P NDynamic load rating C KNEndurance limit Se MpaForce in v-belt (slack side) FB1 NForce in v-belt (Taut side) FB2 NForce on cutting disc FC NLoad factor kc Maximum normal stress σmax MpaMaximum shear stress τmax MpaMiscellaneous factor kf Moment M NmMoment of inertia I m4

Normal stress σ MpaPower input to the arbor shaft Pin WPower output from motor Pout WRadial load Fr NRadius r r mmReaction force on Q in the y-direction Qy NReaction force on Q in the z-direction Qz NReaction force on R in the y-direction Ry NReaction force on R in the z-direction Rz NReliability factor ke Rotational speed n RpmSafety factor FSSecond moment of inertia J m4

Shear force between P and Q VPQ NShear force between Q and R VQR NShear force between R and S VRS NShear stress τ MpaSize factor kb Static load Po NStatic load rating C0 KNSurface factor ka Temperature factor kd Torque T NmUltimate tensile strength Su Mpa

Yielding strength Sy Mpa

1. Introduction

A cut-off is one of the most commonly used machinery in the manufacturing process, and almost every workshop has one. It is easy to use, maintainable and cost effective.

The task was given to a group of engineers in training to design an abrasive cut-off machine for cutting steel. After considering a few concepts, along with a literature study, the final design and calculations were done. Included in the final design are a modelled CAD drawing with detail drawings.

2. User Requirements

An abrasive cut-off machine has to completely designed for cutting steel. It must be able to cut 50mm solid steel and 75mm steel pipes. The cut-off machine should be fitted with safety guards where required and also have an adjustable down stop to the limit the depth of the cut. A mechanism is required for pulling the machine down when someone is cutting.

3. Literature Study

4. Functional Analysis

4.1 System Level

4.2 Mission Level

Long live expectancy Maintainable Reliable Functional Simplicity Safety Productivity Easy to use

4.3 System Level Functional Diagram

4.4 First Level Functional Diagram

4.5 Design Parameters per Function

1.1. Start Motor

1.1.1.Is cutting disc clear of work peace

1.1.2.Press button Start button visible Start button reachable

1.1.3.Pull up Use handle

1.1.4.Press button Start button visible Start button reachable

1.2. Pull Down1.2.1.Pull handle Handle long enough

Hand grip (ergonomics)Enough momentum

1.2.2.Finished cutting Desired cut achieved

1.3. Cutting1.3.1.Hold handle down Handle long enough

Sparks directed backwardsPulley and disc safety guardCutting machine staionary

1.4. Pull Up1.4.1.Press stop button Button visible

Red 1.4.2.Remove work piece Release clamp

1.5. Motor Stop

5. Design Specifications

Basic specifications for abrasive cut-off machine

Symbol Value UnitCutting wheel capacity Ø 304 mmCutting wheel speed nshaft 4000 rpmMotor (Single Phase) Pout 3.75 kWMotor Speed nmotor 2950 rpmHole in Cutting Disc d Ø25 mmUse EN3 steel for shaft Sy 325 MPa

Su 450 MPaTabel 5.1 Basic specifications for abrasive cut-off machine

Assumptions

Symbol Value UnitNo power losses in pulley drive η 1 -Operating temperature T 60 °CMass of shafts and pulley are neglable m 0 kg

Tabel 5.2 Assumptions

Figure 5.1 Schematic drawing for the cut-off machine layout

Figure 5.2 Forces on the cutting disc and pulley.

6. Concepts & Concept Evaluation

Concept 1

Figure 6.1 Concept 1

In the concept the hinge point is situated at the rear of the machine. Pulleys with V-belts will be used to transmit power from the motor to the arbor shaft.

Concept 2

Figure 6.2 Concept 2

In this concept the hinge is located slightly in front of the motor (if the cutting disc is said to be the front), this will act like a “see-saw”. When the machine is not busy cutting steel, the cutting disc will be kept in the air due to the weight of the motor at the back. Pulleys and a V-belt will be used for power transmission.

Concept 3

Figure 6.3 Concept 3

Fixing the cutting disc to the motor shaft directly.

Concept 4

Figure 6.4 Concept 4

The motor will be mounted on a steel plate and the cutting disc mounted on the motor shaft. The plate with the motor will be able to slide between two slots to keep it steady while the motor is pulled up with a chain and pulley or moving down because of the motors weight (and gravity).

Concept Evaluation

Concept 1 Concept 2 Concept 3 Concept 4Simplicity 4 4 4 2Practicability 3 5 2 2Manufacturability 4 4 5 3Maintainability 4 4 5 3Yielding Possibility 4 4 2 2Safety 3 4 1 1Cost 3 3 5 2Able to comply with specs 5 5 1 1Total 30 33 25 16

Table 6.1 Concept Evaluation

Thus from the evaluation, Concept 2 will be the best option.

7. Design calculations

7.1 Power Transmission and Torque.

Power on shaft Pout = ηPin P 3750 W Assume η =1Toque on shaft T = (60P)/(2πn) T 8.95 Nm

7.2 Forces on Pulley

FB1 221 N

FB2 400 N

Ø d 100 mm

T 8.95 Nm

Ø D 300 mm

C 59.67 N

T 8.95 Nm

7.3 Shear Force and Bending Moment

Qy 322.38 N

Ry 883.68 N

Qz 450 N

Rz 150 N

Moment at Q MQ 30.588 Nm

Moment at R MR 46.575 Nm

Shear Force between P & Q VPQ 305.877 N

Shear Force between Q & R VQR 302.517 N

Shear Force between R & S VRS 621 N

7.4 Safety Factor of Shaft (Dynamic)

M 46.575NmT 8.95Nmd 0.025m

Steel Sy 325MPa

Su 450MPa

Te=(M2+T2)1/2 Te 47.42713Nm

τ=16Te/πd3 τ 15458856Pa

τmax= Sy/2FS FS 10.51177

7.5 Safety Factor of Shaft (Fatigue)

From SKF 6305Ø d 25mmØ D 32mm

r 1mm

M 46.575NmT 8.95Nm

Steel Sy 325MPa

Su 450MPa

Endurance Limit

Se’= 0.5Sut Se’ 225 Mpa Sut ≤ 1460 MPa

Surface Factor ka = 4.51 Sut-0.265

ka 0.893 Machined

Size Factor kb=1.24d-0.107 kb 0.879 2.79 ≤ d ≤ 51 mm

Load Factor kc 1 Combined Loading

Temp Effects kd 1 T < 300°C

Reliability ke 0.897 90% ReliabilityMiscellaneous factor kf 1 No Corrosion

Se = kakbkckdkekfS’e Se 158.45 Mpa

Stress Concentration

D/d 1.28

r/d 0.04

Bending

Table A-13-9 (Shigley) Kt 2.1

Fig 6.20 (Shigley) q 0.7

Kf = 1 + q(Kt – 1) Kf 1.77

Torsion

Table A-13-8 (Shigley) Kts 1.7

Fig 6.21 (Shigley) qs 0.85

Kfs = 1 + qs(Kts – 1) Kfs 1.595

Alternating and mean stressesσ a = 32M/πd3 σ a 30.36 MPaσ m = 0 σ m 0.00 MPaτa = 0 τa 0.00 MPaτm = 16T/πd3 τm 2.92 MPa

Combine Components: Trescaσ a’ = ((kf σa)2 + 3(kfsτa)2)1/2 σ a’ 53.74 MPa

σm’ = ((kf σm)2 + 3(kfsτm)2)1/2 σm’ 9.31 MPa

Mean Stress: Asme(nσ’a/Se)2 + (nσ’m/Sy)2 = 1 n 2.94 → FS

7.6 Bearing Calculations

y-component at Q Qy 322.38 N

z-component at Q Qz 450.00 N

Resultant force at Q Q=(Qy2+QZ

2)1/2 Q 553.56 N

y-component at R Ry 883.68 N

z-component at R Rz 150.00 N

Resultant force at R R=(Ry2+RZ

2)1/2 R 896.32 N

Radial force on bearing Fr 896.32 N

Axial force on bearing Fa 0.00 N

Design Temp T 60 °CRotational Speed n 4000.00 rpm

Design for L10h 25000.00 hours

L10h = (C/P)p x (106/60n) C 16.29 kN

→ Choose SKF 6305 Explorer Roller Bearing

From SKF C 23.40 kN

C0 11.60 kNd 25.00 mmD 62.00 mm

Equivalent dynamic bearing load

FA /FR 0.00 N

P = FR P 896.32 N

Equivalent static bearing load

Po = 0.6Fr + 0.5Fa P0 537.79 N

P0 < FR → P0 = FR P0 896.32 N

Static Safety Factor

S0 = C0/P0 S0 12.94 is > 1

Basic Rating Life

L10 = (C/P)p (p=3 for roller bearings) L10 17793.35 Cycles

L10h = L10x (106/60n) L10h 74138.95 hours

Adjusted Rating Life

SKF table 1 p53 a1 1.00 90% Reliability

dm=0.5(d+D) dm 43.50 mm

SKF diagram 5 p60 v1 10.00 mm2/s at dm and 4000 rpmSKF diagram 6 p61 ISO VG 22 at 60°C an d v1

v 24.00 mm2/s at 40°C

ĸ = v/v1 ĸ 2.40

SKF Diagram 1 p54 a23 2.00 at ĸ = 2.4

Lna = a1a23L10 Lna 35586.70 hours Which is sufficient

7.7 Pulley Design

Speed Ratio

n1d1 = n2d2 d2 135.59mm

Round d2 136.00mm

Power Transmission

T = (FB2 – FB1)xd/2 T 8.95Nm

Pre-tension

Fi = (FB2 – FB1)/2 - Fc Fi 89.5N

8. Detail Design

9. Conclusion

10. References

11. Annexure

11.1 Appendix A