Theory of machine question

Gear Box Design for a Corn Seed Separator Machine

Motivation

Corn is one of the most popular food globally. Cornfields typically consist of large areas with hectares of land. Typically, The corn crop cultivation requires huge effort in preparation. The corn seeds has to be separated from the corn bud. But single corn consists of thousands of corn seeds, and in a cornfield, such thousands of corn buts are cultivated. So, there should be a proper method of separating the corn seeds from the corn buds. To do it efficiently and adequately, a corn seed separator machine requirement is needed. There are several types of corn seed separator machines with several methods of separation is done. All these machines have one common thing, which is a gearbox for power transmission. The purpose of having a gearbox is to have various speeds and torque combinations with the input corn but types. Also, it needs to have a reverse gear. If there is any blockage during the machine's running, then we can reverse run the machine and clear the blockage. So, the design of an appropriate gearbox such corn seed separator machine is a valuable task.

Literature review

Various research has been conducted to discuss the design of gear wheels and gear boxes. As per Khurmi, R. and Gupta, J., 2004. A Textbook Of Machine Design. New Delhi: Eurasia Publishing House Ltd. /Chapter 28 [01], there are two basic types of gear wheels. Cycloidal teeth and Involute teeth. Both have their own advantages and disadvantages. Some papers have stated that the most suitable material to build gear wheels from selected materials. According to [02], considering Aluminium and Steel as the selected materials for design of gear wheels, Aluminium shows lesser stress when applying a load in the Aluminium gear wheel than Steel gear. Also, Aluminium is higher corrosion resistance and less weight than Steel.

Design & Analysis

Two meshing gears have wheel and a pinion which the wheel is larger gear, and the pinion is smaller gear. Finding the minimum pinion teeth and the module of the gear wheel is considered in this calculation. Here we need to determine the minimum no. of teeth of pinions to avoid interference. Here the calculation is done only to one pair of gear wheels. In the same manner we can calculate for the other gear ratios as well. Also, involute profiled gear teeth are considered in this analysis.

Figure ‎31 pinion and Wheel

Figure ‎32 Terms used in gears

Data:

Gear ratio of gear pair 4

Pressure angle (ѱ) = 200

pinion material – Gray cast Iron (450 MP)

wheel material – Malleable Cast Iron (350MP)

Assumptions:

Spur gears have teeth with involute profile.

Formulae:

T= 2/(√G2+(1+2G)(sin20)2−G)

Where

T -the number of teeth in the pinion.

G- Gear ratio

Calculations:

T>= 2/(√G2+(1+2G)(sin20)2 −G)

T>= 2/(√42+(1+2*4)(sin20)2 −4)

T>=15.44

T =16

So, the number of the teeth in the wheel is 4*16=64

Take Power transmitted = 5hp =3.677kW

Take Rpm = 125rpm = 13.08rads-1

For the pinion,

d (diameter)= m×T

take m (module) as 3.

d = 3*16

d =0.048m

power = torque*(rpm)

3677 = (foece*radius)* (rpm)

3677 = (F*0.024)*13.08

Force = 11,713N

To design the gear wheels, this force (load on pinion) should be greater than the strength of the

pinion.

Finding the strength of the pinion.

For pinion,

y p(form factor) = 0.154 - 0.912/T

y p = 0.154 - 0.912/16

= 0.107

For wheel,

y w(form factor) = 0.154 - 0.912/T

y w = 0.154 - 0.912/64

= 0.13975

For pinion,

(Q0* y p )p = 450*0.107 = 48.15 MP

For wheel,

(Q0* y w )w = 350*0.13975 = 48.92MP

So, the pinion is weaker than the wheel. So, we need to design for the pinion.

Design strength of the pinion.

Cv = 3/(3+v)

Cv = 3/(3+0.26)

Cv = 0.92024

F = {allowable static stress} * Cv * m * 10m * π

F = 48.15 MP * 0.92024* 3* (10*3)* π

F = 12,528N > (11,713N, the force acting on the pinion)

So, the Force is less than the strength.

It is suitable to use a 3mm module for the pinion.

References

[01] Khurmi, R. and Gupta, J., 2004. A Textbook Of Machine Design. New Delhi: Eurasia Publishing House Ltd. /Chapter 28

[02] P.B.Vavhal, K. C More and A.A. Patil., Design and Development of Spur Pinion in Loading Condition with Different Material

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