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Worm-Worm Gear and the Shaft Deflection

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Project Problem: A winch, seen schematically below, is driven by a series of worm-worm gears. An electric motor that rotates at 18,00rpm gives the input torque to the worm. The speed at which the worm gear is required is between 40 and 50 pm. The winch’s maximum torque requirement is around 4,800 lbs, the atmospheric working temperature is 120 ° F, and the average production power does not exceed 1.33 hp. The following measurements were performed knowing that the winch drum radius is 8 in and that the winch runs 3 to 4 hours a day:

Executive Summary​​ 

Worm gears are utilized on behalf of transmitting power among two non-parallel, non-converging shafts. The high ratio of equipment is about 200:1 can be got. The geometry of a worm is like with the purpose of a power rotation.​​ The pivot of a worm mimics a straightly progressing involutes rack; the presentation of a worm gear is like a helical rigging; aside from that, teeth are bent to wrap the worm. A pole is a pivoting part used to transmit power or movement as a rule of the​​ roundabout cross area. It gives the pivot of revolution, or wavering, of components that control the geometry of their motion, such as gears, pulleys, flywheels, wrenches, sprockets, and so on. A pivot is a non-turning component that transmits no torque and is used to help pivot wheels, pulleys, and so on. Numerous pole outline circumstances incorporate an issue of transmitting torque starting with one component then onto a next pole.

The plan must be examined from the accompanying perspectives:​​ 

1. Deflection

a) Deflection of Winding​​ 

b) Deflection of Tensional​​ 

c) Slope at course along with shaft-bolstered components.​​ 

d) Shear Deflection because of transverse stacking of small shaft.​​ 

2. Stress​​ 

a) Stationary quality​​ 

b) Exhaustion quality​​ 

1) Plan the collection of worm-worm gear that satisfies the winch activity criteria (i.e., conducting analyses of power, stretching, and wear for the gear set). For the gear teeth, expect a design​​ factor of 1.1 and make sure the mesh is self-locking).​​ 

Solution:​​ 

N1= 1800rps

T1​​ & T2​​ = 40 &50

d1= d2=​​ 16

 

Assume = p=10

= = = 0.3978

=0.3978

 

21.69

Helix angle = 90-

Helix angle =68.31

P1=, P2=,

P1​​ =​​ 1.256, P2= 1.0048

2). Design the Shaft for stress and the deflection constrains, that will support the worm gear​​ 

The Design of the Shaft for the stress is given as below​​ 

= ​​ , =​​ 

= ​​ , = ​​ 

Whereas the,​​ are the alternating bonding,​​ ​​ are the alternating torques​​ are the fatigue stress​​ 

Suppose the solid shaft on the behalf of the round cross section in the specific geometry for the c, I, J.​​ 

= ​​ , =​​ 

= ​​ , = ​​ 

MATLAB Code for Desing worm-Worm gear inputs​​ 

w1=input('enter the value w1:'1800);

w2=input('enter the value w2:'4800);

D=input('enter the value D:'16) ;

L=input('enter the value L:'8);​​ 

E=207000;%Young's​​ 

g=9810;​​ 

b11=600;b22=500;b12=275;b21=275;​​ 

x11=175;x22=275;x12=175;x21=175;​​ %lengths of shaft before load point​​ 

I=pi*(D^4)/64 ;

FR=6*E*I*L;

d11=b11*x11*(L^2-b11^2-x11^2)/FR ;

d22=b22*x22*(L^2-b22^2-x22^2)/FR ;

d21=b21*x21*(L^2-b21^2-x21^2)/FR ;

​​ d12=b12*x12*(L^2-b12^2-x12^2)/FR;

Y1=w1*d11+w2*d12;

Y2=w1*d21+w2*d22;

EWY=w1*Y1+w2*Y2;

EWY2=w1*Y1*Y1+w2*Y2*Y2;

w=sqrt(g*EWY/EWY2);

The output of this code will shown in your workspace​​ 

Drawing for designing shaft:​​ 

Figure: 1​​ 

​​ 

Figure 2:​​        Figure 3:​​ 

 

 

Figure: 4

 ​​ ​​ ​​ ​​​​ Explanation​​ 

Figure 1 shows the gear's assembly, where the equipment is constrained during a kinematic loop, which is offered in the closed-loop topology on behalf of eth worm-worm gear. As you can see, the worm and the gear constrain block can connect with the gear body and the worm body by eliminating freedom. Figure 2 shows that the configuration of the eth shaft supports the worm gear for the speed reducer. Figure 3 also shows the structure of posts that support and move the two equipment and two bearings. Figure 4​​ specifies the integrals pinion with the three shoulders of the bar and the sleeves​​ 

Conclusion:​​ 

In this project, we learn about the Worm-Worm gear and the shaft deflection as we know that about the gear inputs, which is also showed in the MATLAB code. Shaft design for the stress.

 

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