Calculations
Velocity locity Ratio = VR =
. ℎ . ℎ
=
2 2 /
=
=
2×17.5 2×35/40
= 20 (This is a
constant), m prove another calculation only for 1 st Exper Exper i ment ment;;
15
Mechanical nical Adva Advantage= MA =
Mechanica nical Effi Efficiency = ɳ = =
We cannot calculate Input work and and output work because because we did not measure the X and Y in the Practical ideal effort ffort and friction friction effort because ideal effort can calcul calcula ate only for f or ɳ =1, =1,
=
=
=
12
= 1.25
ℎ
=
. .
=
1.25 20
= 0.0625
Results VR = 20;
Test
1
2
3
4
5
6
7
8
9
10
Applied Load (F)
15
25
35
45
55
65
75
85
95
105
Actual Effort (Ea)
12
14
17
19
22
24
27
29
32
34
Mechanical Advantage (MA) Mechanical Efficiency (ɳ )
1.25
1.7857
2.058
2.368
2.5
2.7083
2.777
2.931
2.9687
3.0882
0.0625 0.08928 0.1029 0.1184 0.125 0.13541 0.13885 0.14655 0.148435 0.15441
Actual Effort(N) 40 35
34 32
30
29 27
) N25 ( t r o f f 20 E l a u t c 15 A
24 22 19 17 14 12
10 5 0 0
20
40
60
Applide Lode (N)
80
100
120
Discussion A. Objectives of the Experiments
Worm and Worm Gear It . Worm and worm wheel consists of a square threaded screw (known as worm) and a toothed wheel (known as worm wheel) geared with each other. A wheel is attached to the worm, over which passes a rope a load is securely mounted on the worm wheel.
Lodes We use Lodes to compare both side. we input the lode in to worm wheel and compare with other side and applied lode to worm gear. After that worm gear was shifted in some lode and we got that point lord as an Actual effort. We use N lodes in 2N 20N range.
Vernier Caliper We have to use that for get length correctly worm gear and worm wheel. But we didn Verni er Cali per
Ruler We use the ruler for measure the length of worm gear and, diameter of worm wheel.
Worm Drive s Types There are three different types of gears that can be used in a worm drive. The first are non-throated worm gears. These don't have a throat, or groove, machined around the circumference of either the worm or worm wheel. The second are single-throated worm gears, in which the worm wheel is throated. The final type are double-throated worm gears, which have both gears throated. This type of gearing can support the highest loading. An enveloping (hourglass) worm has one or more teeth and increases in diameter from its middle portion toward both ends. Double-enveloping worm gearing comprises enveloping worms mated with fully enveloping worm gears. It is also known as globoidal worm gearing.
Left Hand side and Rite hand side Worm A right hand helical gear or right hand worm is one in which the teeth twist clockwise as they recede from an observer looking along the axis. The designations, right hand and left hand, are the same as in the long established practice for screw threads, both external and internal. Two external helical gears operating on parallel axes must be of opposite hand. An i nternal helical gear and i ts pinion must be of t he same hand. A left hand helical gear or left hand worm is one in which the teeth twist anticlockwise as they recede from an observer looking along the axis.
B. The Effects of 1 to 10 starts on the worm on VR, M,
ɳ and the Low of the Machine
Mechanical Advantage A machine is usually designed so that the load overcome is greater than the effort applied. The ratio of load to effort is known as the mechanical advantage of the machine. Therefore Load M echani cal Ad vantage = Lor d/ Effort
In an ideal machine there is no friction and the ratio load/ideal effort is then called the ideal mechanical advantage. In practice the actual mechanical advantage is always less than the ideal and is obtained by experiment.
The Effort - Load graph the law of the machine If an experiment is carried out on a machine to determine the effort (E) required to lift a load (F) for a range of values of the load then a straight line is usually obtained. Since the graph is a straight line, the relation between E and F may be represented by the equation ; where a and b are constants which are obtained fr om the graph. E = aF + b This equation is known as the law of the machine
The Mechanical advantage - Load curve A graph of mechanical advantage against load can be plotted from experimental values. From such a graph the mechanical advantage at any load may be obtained. Usually the mechanical advantage increases with load but there is no straight line relationship between these two quantities.
Friction effort The effort required at any particular load to overcome friction alone is called the friction effort. The actual effort E required at any load is made up of two parts: 1. The effort required to move the load if the machine was ideal 2. The effort to overcome friction Therefore; fri cti on effort = actual effort
ideal effort
Usually the friction effort increases li nearly wi th load, but the increase in friction effort is not as great as the corresponding increase in load.
Velocity Ratio To obtain a mechanical advantage greater than unity, the effort must move through a greater distance than that through which the load moves. Since the distances moved by the load and effort take place at the same time, the ratio of these distances is the same as the ratio of the velocities. The velocity ratio of the machine is therefore defi ned as: velocit y rat i o = D i stan ce moved by eff ort / D i stan ce moved by lode
The velocity r ati o of a machine usually remains constant for all loads. Using the principle of work, it can be shown that for an ideal machine the velocity ratio is equal to the ideal mechanical advantage. But note that for a real machine the velocity ratio is not the same as the mechanical advantage since there is always some friction present and the actual mechanical advantage is always less than the ideal.
Efficiency The efficiency of a machine is defined as the ratio of the useful work done by the machine to the actual work put into the machine. It can be shown that: eff i ci ency = η = M echani cal advant age / V elocity r ati o
For a simple machine, efficiency usually increases with load until it reaches a limiting value. C. Experiment Result Compare with Calculated data We get the readings as an Actual effort. And we draw a graph between applied lode and actual effort. We have to get a graph like strait line but the case is that graph is not exactly linear. It tangential shape because of worm wheels friction and our humil ity disappoints.
D. Discrepancies or unusual features We Have discrepancies about our calculation data and measuring data. we have to calculate E 1 (Ideal Effort) but we enough details for calculate it. Because our Applied lode range is small. We can calculate E1 only for ɳ =1; but our Velocity Rati o is 20, and we have to find M A (Mechanical Efficiency) = 20 to applied lode and ideal effort. Then we have to apply large lode to our Machen. It is impossible because our experiment Machen is small. And also we can t calculate fr iction effort. We measure the X and Y lengths because it is difficult to measure. Then we can work and output work. Worm and Worm wheel is madein plasti cs, then our friction effort will be high. After the doing practical we have to choose a point to start the practical.
E.
Limiting efficiency for each gear set
Comparing efficiencies of di fferent gear types across various reduction rati os will help us to make right gearbox selection for our applications. These efficiency values are for general guideline and refer manufacturers catalogue for more accurate values.
No
Type
Normal Ratio Range
Effi ciency Type
1 2 3 4 5 6 7
Supper Straight level Spiral Bevel Worm Hypoid Helical Cycloid
1:1 to 6:1 3:2 to 5:1 3:2 to 4:1 5:1 to 75:1 10:1 to 200:1 3:2 to 10:1 10:1 to 100:1
94% - 98% 93% - 97% 95% - 99% 50% - 90% 80% - 95% 94% - 98% 75% - 85%
Most important gear type is worm gear type, because it has a theoretical calculation. Worm gear efficiency varies significantly when lead angle, friction factor and gear ratio changes. Worm Gear Efficiency Calculation
Use the following gear efficiency equation to calculate efficiency of worm gears.
f - the coefficient of friction for worm gears (normally ranges from 0.06 to 0.02) P - the pitch of the worm thr ead r - the mean radius of the worm.
Conclusion Worm and worm wheel i s a simple Machin t o use calculate the friction effort. It s madein plasti cs. After all Instructor was giving rough idea for us about worm and worm wheel. Then we change the applied lode (F) and get the readingsnamed actual effort (E a). Next we calculate the Mechanical advantage (M A), Mechanical efficiency ( ɳ ) and Velocity Rati o (VR). During the lab section we haven measure X and Y because it little bit difficult. Then wehave problem to calculate Input work and Output work. And also we haven calculated Ideal effort (Ei) and Friction effort (Ef ) because our Velocity ratio is higher than Mechanical advantage then we can t get ɳ =1 and also we apply up to 105N lodes because our Machen is small. Before these calculations we draw a graph using E a = a.F+b equation. Last of the practical we were made a lab report.
References
The theory & practice of worm gear drivesIn-text: (Dud s) Dud s, Ill s. The Theory & Practice Of Worm Gear Drives. 1st ed. London: Kogan Page Science, 2004. Print.
Fundamentals
of
kinematics
and
dynamics
of
machines
and
mechanismsIn-
text: (Vinogradov) Vi nogradov, Oleg. Fundamentals Of Ki nemati cs And Dynamics Of Machines And Mechanisms. 1st ed. Boca Raton: CRC Press, 2000. Print.
