Copy of Agarbatti Maker Designing and Analysiss

Design Parameters:

Following are the design parameters for analysis of pinion.

InputParameter Value Unit

Force for Extrusion 4908.666667

N

Pinion diameter 45 mm

Face width 1.653 in

pressure angle 20 Degrees

Quality of gear 8

Bending failure analysis of teeth.Input parameters

Input (Pinion tooth failure)

Parameter ValueUnit

Force on pinion (F_t)4908.6

6 NK_o 1 No. of teeth 15 K_B 1 J (from chart) 0.42 Y_N 1 K_T 1 K_R 1 Safety factor (S_F) 1.1 Quality of gear 8

Pinion diameter for pinion 1 (P_d) 45mm

Relations used,

where ,W t=Load on pinion toothPd=Diametral PitchF=Facewidth of gear teeth

σ bending=WtK oK v

Pd

F

KmKB

J

where ,SF=Safety factor for Pinion tooth∈bendingKT=Thermal factorK R=Reliability Factor

St=(Desired value)

Here, calculations were done for different gear diameters keeping force on pinion and values for st were found so that a proper gear material can be decided.

Putting values in above relations, we obtained following output results,

Output(Pinion tooth failure)

Parameter ValueUnit

Bending stress17.14408

555kpsi

S_t18.85849

41kpsi

S_t(Mpa)130.0104

583Mpa

Contact failure analysis of teethInput Parameters

Input (Pinion tooth failure)Parameter Value UnitForce on pinion (F_t) 4908.66 N

Pressure angle 20Degrees

K_s 1 K_o 1 No. of teeth 15 C_f 1 I 1 Z_N 1 K_T 1 K_R 1 Safety factor (S_F) 1.1

SF=(S¿¿ t

Y N

KT KR

)

σbending¿

Quality of gear 8 Pinion diameter for pinion 1 (d_p) 45 mm

d_p1.7716535

43 in

C_p 2300psi^1/2

C_h 1

Relations used,

where ,W t=Load on pinion toothdp=Pitch diameterF=Facewidth of gear teeth

wher e ,SH=Safety factor for Piniontooth∈bendingKT=Thermal factorK R=Reliability Factor

Sc=(Desired value)

Here, calculations were done for different gear diameters keeping force on pinion and values for st were found so that a proper gear material can be decided.

Putting values in above relations, we obtained following output results,

Output(Pinion tooth failure)Parameter Value UnitContact stress 50.39 kpsiS_c 55.43 kpsiS_c(Mpa) 382.15 Mpa

Design (Bending +Torsion)

σ contact=Cp∗(Wt∗Ko∗K v∗Ks∗K mC f

I∗F∗d p)

12

SH=

Sc∗Z N∗Ch

KT KR

σContact

Shaft With Gear 1

F_t (N) F_r (N)Torque on shaft

Max(bending moment)

Sigma (net)

N-m N-m

490 178.6 12.27126.0767118

310500000

0

Diameter of shaft

0.013981 m

13.9813

6 mm

Shaft With Gear 2&3

Gear1 Gear 2

F_t (N) F_r (N) F_t (N) F_r (N)Torque on shaft (N-m)

Max(bending moment)

Sigma (net)

490 178.6 1636 595.4 139.77 108.281.05E+

08

Diameter Diameter(mm)

0.025073 25.07336661

Shaft With Gear 4&5

S_y 2.1E+08 Mpa S.F 2 Sigma (allowable) 1.05E+08

Gear4 Gear 5

F_t (N) F_r (N) F_t (N) F_r (N)Torque on shaft (N-m)

Max(bending moment)

Sigma (net)

1636 595.3 4908 1786 220.86 177.78 1.05E+08

Diameter Diameter(mm)0.02937

4 29.37405342

Bearings analysis

Analysis was done for four bearings as shown in figure,

Load on bearings 1 & 2, notation ‘X’ means into the plane, ‘O’ means out of plane.

Appling force and moment balance, on bearings 1 and 2,

¿ formula,L=K R( C10

K A P )a

where ,L=Life∈million cyclesK R=Reliability factor

K A=Application factorP=Radial Load onbearing

For above bearings, loads were calculated and they came out to be,

1

3

2

P_A

P_B

X O1 2

Bearing 1,

(P¿¿ A)=4.36kN ¿(PB )=0.595 kN

From equation above, C10=40.44 kNBearing 2,

(P¿¿ A)=2.18 kN ¿(PB )=0.992kN

From equation above, C10=27.11kN

For bearing 3 & 4,

Bearing 3,

(P¿¿ A)=1.86 kN ¿(PB )=3.94 kN

From equation above, C10=58.36kN

Bearing 4,

(P¿¿ A)=1.56 kN ¿(PB )=1.56 kN

From equation <>, C10=27.11kN

Bore size = 24.00 mmOuter Diameter = 55.000 mmWidth = 25.00 mmLoad rating – 49.54kNType –Single-Row tapered roller bearings

(From online catalog mentioned in

Bore size = 26.988 mmOuter Diameter = 62.00 mmWidth = 19.05 mmLoad rating – 53.00 kNType –Single-Row tapered roller bearings(From online catalog)

F r

F t

F r(O)

F t(O)

3 4

Design 2

Design OverviewThis design consists of power screw mechanism coupled with nut type gear coupled with spur gears which are further engaged with bevel gear. Power screw mechanism will be used to apply extrusion force on slurry or paste material in the <> mm diameter nozzle as described in design 1.

Nut type Gear with external

Direction of motion/force of screw

Basic assumptions We have neglected the forces on members due to weight of each component. This assumption

is not quite reasonable for actual final designing of machine but it works well here as we are doing gear tooth analysis only.

We have neglected the effects due to helix angle of screw. This assumption is valid for most practical purposes.

Pressure to be applied on paste is assumed to be constant (10 MPa). Although value of pressure seems wrong, the procedure of analysis is what is important. Analysis will be done at the extreme conditions of forces.

MechanismMechanism consists of screw applying force vertically and is driven by spur-gear as shown in figure 2.

Handle

Bevel Gears

Direction of force

1

3

2

5

4

R

Here, Gear 1 is driving screw downwards. Bevel gears 3 & 4 are just for converting direction of rotation comfortable to user. Here, more gear stages can be added between 1 and 2 as above diagram is only representative. For actual design, for example, gear 4 can be smaller than 3.

Design Parameters & Calculations Following are the design parameters chosen for analysis of screw,

Input

Parameter Value Unit

Force for Extrusion 4908.666667 N

Dscrew 2 in

pitch 0.25 in

Lead 0.25

alpha 14.5 Degrees

Friction factor (f) 0.11

From relation of Torque required raising the load,

.. (1)

Calculating torque,

T R=981.3Nm

This torque has to be applied on gear 1, Parameters for gear tooth analysis (Gear 1) are,Force on pinion teeth was calculated by relation

F t=T R

d

Here, calculations were done for different gear diameters keeping force on pinion and values for st were found so that a proper gear material can be decided.

Input (Pinion tooth failure)Parameter Value UnitForce on pinion (F_t) 10930.4418 N

T R=F dm

2 ( 1+πf dm secαπ dm−flsecα )

K_o 1 No. of teeth 60 K_B 1 J (from chart) 0.42 Y_N 1 K_T 1 K_R 1 Safety factor (S_F) 1.3 Quality of gear 8 Pinion diameter for pinion 1 (d) 180 mm

Relations used,

..(2)

where ,W t=Load on pinion toothPd=Diametral PitchF=Facewidth of gear teeth

..(3)

where ,SF=Safety factor for Pinion tooth∈bendingKT=Thermal factorK R=Reliability Factor

St=(Desired value)

Putting values in above relations, we obtained following output results,

Output(Pinion tooth failure)

Parameter Value Unit

Bending stress 52.98 kpsi

σ bending=WtK oK v

Pd

F

KmKB

J

SF=(S¿¿ t

Y N

KT KR

)

σbending¿

St 58.29 kpsi

St (Mpa) 401.83 Mpa

Stress factor comes out to be 58.29 kpsi.

Gear ratio/No. of stages required calculationsGear ratio has to be decided on the basis of maximum force can be applied by hand casually i.e. 100N. The arm length or radius of disk 5 has been assumed to be 40 cm (Shown in figure <>).

Let the module of gear be 3 mm. and at each stage, reduction takes place of factor of 5. A schematic of one stage has been shown in fig <>. If these stages are put in sequence, required gear ratio can be obtained.

Input parameters required were,

Input (Gear ratio) Parameter Value UnitTorque at stage 1 981.30976 NArm Length 0.4 m

No. of stages 5 Gear reduction per stage (max. 10) 5

After iterations, No. of stages required = 5Force to be applied by arm = 98.13 N (<100N)

So, all our design requirements are met, we have reasonable type of gear to be used and reasonable force required to be applied by hand.

Comparison between Design 1 and Design 2Above design shows picture as compared to design 1 as the pinion forces are within range for this design but are greater than whereas, they were lower in case of Design 1. Also, Design 2 a very high reduction in gear ratio. This will lead to more rotation required at handle side to move screw by small amount. This may lead to fatigue of operating person if operated for long time.

Design 2 can be only useful when the process needs to be automated not manual. In Design 1, force has to be applied with impact whereas, in design 2, it can be easily applied by some servo motor because of high gear reduction.

Design 3

Pneumatic driven mechanism (ONLY Qualitative design)

Component marked A is pneumatic actuator. End of A is connected to lever that drives handle of agarbatti maker.

This circuit can be used to make a small scale machine that may be used small scale production. 5 way spool valve controls direction of motion of actuator rod. This valve is controlled by a

electromagnet. This system is very appropriate for high pressure application like this agarbatti maker. This system will be highly efficient in terms of production rate.

Conclusions Reason for failure for previous design of agarbatti machine gear was poor material as well as

stress concentration at the hole radially drilled across the gear.

ASTM A536 Grade 120-90-02 should be used as Pinion material as per the gear tooth calculations (with safety factor of 1.1).

Design 1 proves to be more efficient and effective if this has to be operated by hand. Design 2 can be proposed as the automatic machine design driven by servo motor. Design 3 is a pneumatic design proposed without any quantification or analysis. It can only be

used for mass production.

Learning Outcomes We learned about failure of gear tooth and its impact on a practical machine. We learned the practical considerations that should be taken care of during iterating, like force

that can be applied by hand. Learned how to select bearings from various catalogs as per the shaft diameter. Got feel for the numbers as we tried to judge them as per design like Pressure required for

extrusion.

Work Load Distribution Prashant Bhatewara – Analysis and design for Design 1 Nakul Nuwal - Analysis and design for Design 2 Prateek Nyati - Analysis and design for Design 3; Material Selection shaft analysis and

conclusions.

Software Used Autodesk Inventor MS Excel. MS Word

References Shigley’s Mechanical Engg. Design, 9th edition. http://www.coroll.sk/Coroll/NSK_katalogy_files/Rolling_Bearings_UK.pdf http://vadodara.olx.in/agarbatti-making-machine-fully-automatic-iid-215446318

http://hydraulicspneumatics.com/other-technologies/chapter-14-sequence-valves-and-reducing-valves

http://www.ejsong.com/mdme/memmods/MEM30009A/lifting_systems/lifting_systems.html http://commons.wikimedia.org/wiki/File:Rack_and_pinion.png

Gear Analysis(a) Bending fatigueWt (Newtons)= 10000module (mm)= 6face width (mm)= 40dynamic factor= 1overload factor= 2backup ratio, mB= 1.583333333rim thickness factor, 1

KB=reliability factor (90%)=

0.85

temp factor= 1stress cycle, YN= 2load distribution factor=

1

size factor= 1surface condition 1.2geometry factor, J= 0.22Grade 1, St for 200 HB=

197.4 Mpa

S.F= S_all/SigmaS_allowable= 464.4705882 MPaSigma, bending= 454.5454545S.F.= 1.021835294