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QUAID-E-AWAM UNIVERSITY OF ENGINEERING, SCIENCE & TECHNOLOGY, NAWABSHAH SINDH.

Grass Cutting Machine Gear Design

Machine Design & CAD - II POWER TRANSMISSION SYSTEM DESIGN PROJECT REPORT

5/12/2010

KHALIL RAZA BHATTI 07ME40

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Introduction GRASS CUTTING MACHINE:

Content Introduction Problem Definition Project Objectives Design Methodology Working Drawing Conclusion

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IT IS SIMPLY THE MACHINE WHICH CONSIST OF ROTATING

BLADES POWERED BY ELECTRIC MOTOR OR BY HAND, GRASS IS FED AT ITS BACK, THRROUGH THE GEAR MECHANISM IT IS COMPRESSED & SHIFTED TROWARDS FRONT AT ROTATING BLADES WHERE THE GRASS IS CUT.

As it has been stated earlier that our main focus of project is on the design of worm gears so in that connection we need to define what are the worm gears are?

Worm Gears:

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A worm drive is a gear arrangement in which a worm (which is a gear in the form of a screw) meshes with a worm gear (which is similar in appearance to a spur gear, and is also called a worm wheel). The terminology is often confused by imprecise use of the term worm gear to refer to the worm, the worm gear, or the worm drive as a unit. Like other gear arrangements, a worm drive can reduce rotational speed or allow higher torque to be transmitted. The image shows a section of a gear box with a bronze worm gear being driven by a worm. A worm is an example of a screw, one of the six simple machines. A gearbox designed using a worm and worm-wheel will be considerably smaller than one made from plain spur gears and has its drive axes at 90° to each other. With a single start worm, for each 360° turn of the worm, the worm-gear advances only one tooth of the gear. Therefore, regardless of the worm's size (sensible engineering limits notwithstanding), the gear ratio is the "size of the worm gear - to - 1". Given a single start worm, a 20 tooth worm gear will reduce the speed by the ratio of 20:1. With spur gears, a gear of 12 teeth (the smallest size permissible, if designed to good engineering practices) would have to be matched with a 240 tooth gear to achieve the same ratio of 20:1. Therefore, if the diametrical pitch (DP) of each gear was the same, then, in terms of the physical size of the 240 tooth gear to that of the 20 tooth gear, the worm arrangement is considerably smaller in volume There are three different types of gears that can go in a worm drive.

The first are non-throated worm gears. These don't have a throat, or groove, machined around the circumference around 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-

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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 wormgearing comprises enveloping worms mated with fully enveloping wormgears. It is also known as globoidal wormgearing.

Problem Definition To examine the design of worm gears of grass cutting machine with its all type of parameters and forces that are responsible to transmit the particular amount of power by these gears and after the calculation of these forces afterwards the right selection of the material that could sustain that load, also determination of individual tooth load it could sustain while transmission of power. Project Objectives

TO UNDERSTAND & DEFINE THE MECHANISM AND THE FUNCTION OF THE GRASS CUTTING MACHINE.

TO EVALUATE THE GEARS USED IN THE GRASS CUTTING MACHINE. THE MAIN TASK OF OUR PROJECT IS TO DESIGN THE WORM GEARS THAT ARE THE ESSENTIAL PARTS WORKING IN THIS TYPE OF MACHINE & PARTICULARLY THE DESIGN OF THE GEARS USED IN IT.

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Design Methodology INTRODUCTION

A worm gear is used when a large speed reduction ratio is required between crossed axis shafts which do not intersect. A basic helical gear can be used but the power which can be transmitted is low. A worm drive consists of a large diameter worm wheel with a worm screw meshing with teeth on the periphery of the worm wheel. The worm is similar to a screw and the worm wheel is similar to a section of a nut. As the worm is rotated the worm wheel is caused to rotate due to the screw like action of the worm. The size of the worm gearset is generally based on the centre distance between the worm and the wormwheel. If the worm gears are machined basically as crossed helical gears the result is a highly stress point contact gear. However normally the wormwheel is cut with a concave as opposed to a straight width. This is called a single envelope worm gearset. If the worm is machined with a concave profile to effectively wrap around the wormwheel the gearset is called a double enveloping worm gearset and has the highest power capacity for the size. Single enveloping gearsets require accurate alignment of the worm-wheel to ensure full line tooth contact. Double enveloping gearsets require accurate alignment of both the worm and the wormwheel to obtain maximum face contact.

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The worm is shown with the worm above the wormwheel. The gearset can also be arranged with the worm below the wormwheel. Other alignments are used less frequently.

Nomenclature

As can be seen in the above view a section through the axis of the worm and the centre of the gear shows that , at this plane, the meshing teeth and thread section is similar to a spur gear and has the same features αn = Normal pressure angle = 20o as standard γ = Worm lead angle = (180 /π ) tan-1 (z 1 / q)(deg) ..Note: for α n= 20o γ should be less than 25o b a = Effective face width of worm wheel. About 2.m √ (q +1) (mm) b l = Length of worm wheel. About 14.m. (mm) c = clearance c min = 0,2.m cos γ , c max = 0,25.m cos γ (mm) d 1 = Ref dia of worm (Pitch dia of worm (m)) = q.m (mm) d a.1 = Tip diameter of worm = d 1 + 2.h a.1 (mm) d 2 = Ref dia of worm wheel (Pitch dia of wormwheel) =( p x.z/π ) = 2.a - d 1 (mm) d a.2 = Tip dia worm wheel (mm) h a.1 = Worm Thread addendum = m (mm) h f.1 = Worm Thread dedendum , min = m.(2,2 cos γ - 1 ) , max = m.(2,25 cos γ - 1 )(mm)

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m = Axial module = p x /π (mm) m n = Normal module = m cos γ(mm) M 1 = Worm torque (Nm) M 2 = Worm wheel torque (Nm) n 1 = Rotational speed of worm (revs /min) n 2 = Rotational speed of wormwheel (revs /min) p x = Axial pitch of of worm threads and circular pitch of wheel teeth ..the pitch between adjacent threads = π. m. (mm) p n = Normal pitch of of worm threads and gear teeth (m) q = diameter factor selected from (6 6,5 7 7,5 8 8,5 9 10 11 12 13 14 17 20 ) p z = Lead of worm = p x. z 1 (mm).. Distance the thread advances in one rev'n of the worm. For a 2-start worm the lead = 2 . p x R g = Reduction Ratio q = Worm diameter factor = d 1 / m - (Allows module to be applied to worm ) µ = coefficient of friction η= Efficiency Vs = Worm-gear sliding velocity ( m/s) z 1 = Number of threads (starts) on worm z 2 = Number of teeth on wormwheel

Worm gear design parameters

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Worm gears provide a normal single reduction range of 5:1 to 75-1. The pitch line velocity is ideally up to 30 m/s. The efficiency of a worm gear ranges from 98% for the lowest ratios to 20% for the highest ratios. As the frictional heat generation is generally high the worm box is designed disperse heat to the surroundings and lubrication is and essential requirement. Worm gears are quiet in operation. Worm gears at the higher ratios are inherently self locking - the worm can drive the gear but the gear cannot drive the worm. A worm gear can provide a 50:1 speed reduction but not a 1:50 speed increase....(In practice a worm should not be used a braking device for safety linked systems e.g hoists. . Some material and operating conditions can result in a wormgear backsliding ) The worm gear action is a sliding action which results in significant frictional losses. The ideal combination of gear materials is for a case hardened alloy steel worm (ground finished) with a phosphor bronze gear. Other combinations are used for gears with comparatively light loads.

Specifications

BS721 Pt2 1983 Specification for worm gearing Metric units. This standard is current (2004) and provides information on tooth form, dimensions of gearing, tolerances for four classes of gears according to function and accuracy, calculation of load capacity and information to be given on drawings.

Worm Gear Designation

Very simply a pair of worm gears can be defined by designation of the number of threads in the worm ,the number of teeth on the wormwheel, the diameter factor and the axial module i.e z1,z2, q, m . This information together with the centre distance ( a ) is enough to enable calculation of and any dimension of a worm gear using the formulea available.

Worm teeth Profile

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The sketch below shows the normal (not axial) worm tooth profile as indicated in BS 721-2 for unit axial module (m = 1mm) other module teeth are in proportion e.g. 2mm module teeth are 2 times larger

Typical axial modules values (m) used for worm gears are

0,5 0,6 0,8 1,0 1,25 1,6 2,0 2,5 3,15 4,0 5,0 6,3 8,0 10,0 12,5 16,0 20,0 25,0 32,0 40,0 50,0

Materials used for gears

Material Notes applications Worm

Acetal / Nylon Low Cost, low duty Toys, domestic appliances,

instruments

Cast Iron Excellent machinability, medium friction.

Used infrequently in modern machinery

Carbon Steel

Low cost, reasonable strength

Power gears with medium rating.

Hardened Steel

High strength, good durability

Power gears with high rating for extended life

Wormwheel Acetal /Nylon Low Cost, low duty Toys, domestic appliances,

instruments

Phos Bronze

Reasonable strength, low friction and good compatibility with steel

Normal material for worm gears with reasonable efficiency

Cast Iron Excellent machinability, Used infrequently in modern

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medium friction. machinery

Design of a Worm Gear

The following notes relate to the principles in BS 721-2 Method associated with AGMA are shown below..

Initial sizing of worm gear.. (Mechanical)

1) Initial information generally Torque required (Nm), Input speed(rpm), Output speed (rpm). 2) Select Materials for worm and wormwheel. 3) Calculate Ratio (R g) 4) Estimate a = Center distance (mm) 5) Set z 1 = Nearest number to (7 + 2,4 SQRT (a) ) /R g 6) Set z 2 = Next number < R g . z 1 7) Using the value of estimated centre distance (a) and No of gear teeth ( z 2 )obtain a value for q from the table below 8) d 1 = q.m (select) .. 9) d 2 = 2.a - d 1 10) Select a wormwheel face width b a (minimum =2*m*SQRT(q+1)) 11) Calculate the permissible output torques for strength (M b_1 and wear M c_1 ) 12) Apply the relevent duty factors to the allowable torque and the actual torque 13) Compare the actual values to the permissible values and repeat process if necessary 14) Determine the friction coefficient and calculate the efficiency. 15) Calculate the Power out and the power in and the input torque 6) Complete design of gearbox including design of shafts, lubrication, and casing ensuring sufficient heat transfer area to remove waste heat.

Initial sizing of worm gear.. (Thermal)

Worm gears are often limited not by the strength of the teeth but by the heat generated by the low efficiency. It is necessary therefore to determine the heat generated by the gears = (Input power - Output power). The worm gearbox must have lubricant to remove the heat from

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the teeth in contact and sufficient area on the external surfaces to distibute the generated heat to the local environment. This requires completing an approximate heat transfer calculation. If the heat lost to the environment is insufficient then the gears should be adjusted (more starts, larger gears) or the box geometry should be adjusted, or the worm shaft could include a fan to induced forced air flow heat loss.

Formulae

The reduction ratio of a worm gear ( R g )

R g = z 2 / z 1

eg a 30 tooth wheel meshing with a 2 start worm has a reduction of 15 Tangential force on worm ( F wt )= axial force on wormwheel

F wt = F ga = 2.M 1 / d 1

Axial force on worm ( F wa ) = Tangential force on gear

F wa = F gt = F wt.[ (cos α n - µ tan γ ) / (cos α n . tan γ + µ ) ]

Output torque ( M 2 ) = Tangential force on wormwheel * Wormwheel reference diameter /2

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M 2 = F gt* d 2 / 2

Relationship between the Worm Tangential Force F wt and the Gear Tangential force F gt

F wt = F gt.[ (cos α n . tan γ + µ ) / (cos α n - µ tan γ ) ]

Relationship between the output torque M 2and the input torque M 1

M 2 = ( M 1. d 2 / d 1 ).[ (cos α n - μ tan γ ) / (cos α n . tan γ + µ ) ]

Separating Force on worm-gearwheel ( F s )

F s = F wt.[ (sin α n ) / (cos α n . sin γ + µ .cos γ ) ]

Efficiency of Worm Gear (η ) The efficiency of the worm gear is determined by dividing the output Torque M2 with friction = µ by the output torque with zero losses i.e µ = 0 First cancelling [( M 1. d 2 / d 1 ) / M 1. d 2 / d 1 ) ] = 1 Denominator = [(cos α n / (cos α n . tan γ ] = cot γ

η = [(cos α n - µ tan γ ) / (cos α n . tan γ + µ ) ] / cot γ

= [(cos α n - µ .tan γ ) / (cos α n + µ .cot γ )]

Sliding velocity ( V s )...(m/s)

V s (m/s ) = 0,00005236. d 1. n 1 sec γ = 0,00005235.m.n (z 1

2 + q 2 ) 1/2

Peripheral velocity of wormwheel ( V p) (m/s)

V p = 0,00005236,d 2. n 2

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Friction Coefficient

Cast Iron and Phosphor Bronze .. Table x 1,15 Cast Iron and Cast Iron.. Table x 1,33 Quenched Steel and Aluminum Alloy..Table x 1,33 Steel and Steel..Table x 2

Friction coefficients - For Case Hardened Steel Worm / Phos Bros Wheel

Sliding Speed

Friction Coefficient

Sliding Speed

Friction Coefficient

m/s µ m/s µ 0 0,145 1,5 0,038 0,001 0,12 2 0,033 0,01 0,11 5 0,023 0,05 0,09 8 0,02 0,1 0,08 10 0,018 0,2 0,07 15 0,017 0,5 0,055 20 0,016 1 0,044 30 0,016

Worm Design /Gear Wear / Strength Equations to BS721

Note: For designing worm gears to AGMA codes AGMA method of Designing Worm Gears The information below relates to BS721 Pt2 1983 Specification for worm gearing � Metric units. BS721 provides average design values reflecting the experience of specialist gear manufacturers. The methods have been refined by addition of various application and duty factors as used. Generally wear is the critical factor..

Permissible Load for Strength

The permissible torque (M in Nm) on the gear teeth is obtained by use of the equation

M b = 0,0018 X b.2σ bm.2. m. l f.2. d 2.

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( example 87,1 Nm = 0,0018 x 0,48 x 63 x 20 x 80 ) X b.2 = speed factor for bending (Worm wheel ).. See Below σ bm.2 = Bending stress factor for Worm wheel.. See Table below l f.2 = length of root of Worm Wheel tooth d 2 = Reference diameter of worm wheel m = axial module γ = Lead angle

Permissible Torque for Wear

The permissible torque (M in Nm) on the gear teeth is obtained by use of the equation

M c = 0,00191 X c.2σ cm.2.Z. d 21,8. m

( example 33,42 Nm = 0,00191 x 0,3234 x 6,7 x 1,5157 x 801,8 x 2 ) X c.2 = Speed factor for wear ( Worm wheel ) σ cm.2 = Surface stress factor for Worm wheel Z = Zone factor.

Length of root of worm wheel tooth

Radius of the root = R r= d 1 /2 + h ha,1 (= m) + c(= 0,25.m.cos γ ) R r= d 1 /2 + m(1 +0,25 cosγ) l f.2 = 2.R r.sin-1 (2.R r / b a) Note: angle from sin-1(function) is in radians...

Speed Factor for Bending

This is a metric conversion from an imperial formula.. X b.2 = speed factor for bending = 0,521(V) -0,2 V= Pitch circle velocity =0,00005236*d 2.n 2 (m/s) The table below is derived from a graph in BS 721. I cannot see how this works as a small worm has a smaller diameter compared to a large worm and a lower speed which is not reflected in using the RPM.

Table of speed factors for bending

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RPM (n2) X b.2 RPM (n2) X b.2 1 0,62 600 0,3 10 0,56 1000 0,27 20 0,52 2000 0,23 60 0,44 4000 0,18 100 0,42 6000 0,16 200 0,37 8000 0,14 400 0,33 10000 0,13

Additional factors

The formula for the acceptable torque for wear should be modified to allow additional factors which affect the Allowable torque M c

M c2 = M c. Z L. Z M.Z R / K C

The torque on the wormwheel as calculated using the duty requirements (M e) must be less than the acceptable torque M c2 for a duty of 27000 hours with uniform loading. For loading other than this then M e should be modified as follows

M e2 = M e. K S* K H

Thus uniform load < 27000 hours (10 years) M e ≤ M c2 Other conditions M e2 ≤ M c2

Factors used in equations

Lubrication (Z L).. Z L = 1 if correct oil with anti-scoring additive else a lower value should be selected Lubricant (Z M).. Z L = 1 for Oil bath lubrication at V s < 10 m /s Z L = 0,815 Oil bath lubrication at 10 m/s < V s < 14 m /s Z L = 1 Forced circulation lubrication Surface roughness (Z R ) .. Z R = 1 if Worm Surface Texture < 3µ m and Wormwheel < 12 µ m else use less than 1 Tooth contact factor (K C This relates to the quality and rigidity of gears . Use 1 for first estimate K C = 1 For grade A gears with > 40% height and > 50% width contact

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= 1,3 - 1,4 For grade A gears with > 30% height and > 35% width contact = 1,5-1,7 For grade A gears with > 20% height and > 20% width contact Starting factor (K S) .. K S =1 for < 2 Starts per hour =1,07 for 2- 5 Starts per hour =1,13 for 5-10 Starts per hour =1,18 more than 10 Starts per hour Time / Duty factor (K H) .. K H for 27000 hours life (10 years) with uniform driver and driven loads For other conditions see table below

Tables for use with BS 721 equations Speed Factors

X c.2 = K V .K R Note: This table is not based on the graph in BS 721-2 (figure 7) it is based on another more easy to follow graph. At low values of sliding velocity and RPM it agrees closely with BS 721. At higher speed velocities it gives a lower value (e.g at 20m/s -600 RPM the value from this table for X c.2 is about 80% of the value in BS 721-2

Table of Worm Gear Speed Factors

Note -sliding speed = Vs and Rotating speed = n2 (Wormwheel)

Sliding speed K V Rotating

Speed K R

m/s rpm 0 1 0,5 0,98 0,1 0,75 1 0,96 0,2 0,68 2 0,92 0,5 0,6 10 0,8 1 0,55 20 0,73 2 0,5 50 0,63 5 0,42 100 0,55 10 0,34 200 0,46 20 0,24 500 0,35 30 0,16 600 0,33

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Stress Factors Table of Worm Gear Stress Factors

Other metal

(Worm) P.B. C.I. 0,4%

C.Steel 0,55% C.Steel

C.Steel Case.

H'd

Metal (Wormwheel)

Bending (σbm )

Wear ( σ cm )

MPa MPa

Phosphor Bronze Centrifugal cast 69 8,3 8,3 9,0 15,2

Phosphor Bronze Sand Cast Chilled 63 6,2 6,2 6,9 12,4

Phosphor Bronze Sand Cast 49 4,6 4,6 5,3 10,3

Grey Cast Iron 40 6,2 4,1 4,1 4,1 5,2 0,4% Carbon steel 138 10,7 6,9 0,55% Carbon steel 173 15,2 8,3

Carbon Steel (Case hardened) 276 48,3 30,3 15,2

Zone Factor (Z)

If b a < 2,3 (q +1)1/2 Then Z = (Basic Zone factor ) . b a /2 (q +1)1/2 If b a > 2,3 (q +1)1/2 Then Z = (Basic Zone factor ) .1,15

Table of Basic Zone Factors q

z1 6 6,5 7 7,5 8 8,5 9 9,5 10 11 12 13 14 17 20

1 1,04 1,04 1,05 1,06 1,08 1,10 1,12 1,13 1,14 1,16 1,202 1,26 1,31 1,40 1,50

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5 8 2 5 4 7 8 7 3 8 2 8

2 0,991

1,028

1,055

1,099

1,144

1,183

1,214

1,223

1,231 1,25 1,28 1,32 1,36 1,44

7 1,575

3 0,822 0,89 0,98

9 1,109

1,209 1,26 1,30

5 1,333 1,35 1,36

5 1,393 1,422

1,442

1,532

1,674

4 0,826 0,83 0,98

1 1,098

1,204

1,701 1,38 1,42

8 1,46 1,49 1,515 1,545 1,57 1,66

6 1,798

5 0,947

0,991 1,05 1,12

2 1,216

1,315

1,417 1,49 1,55 1,61 1,632

* 1,652

1,675

1,765

1,886

6 1,131

1,145

1,172 1,22 1,28

7 1,35 1,438

1,521

1,588

1,625 1,694 1,71

4 1,733

1,818

1,928

7 1,316 1,34 1,37 1,40

5 1,452 1,54 1,61

4 1,704 1,725 1,74 1,76 1,84

6 1,98

8 1,437

1,462 1,5 1,55

7 1,623

1,715 1,738 1,75

3 1,778

1,868 1,96

9 1573 1,604

1,648 1,72 1,743 1,76

7 1,79 1,88 1,97

10 1,68 1,72

8 1,748 1,773

1,798

1,888 1,98

11 1,73

2 1,753 1,777

1,802

1,892

1,987

12 1,76 1,78 1,80

6 1,895

1,992

13 1,78

4 1,806

1,898

1,998

14 1,81

1 1,9 2

Duty Factor Duty - time Factor K H

Impact from Prime mover

Expected life hours

K H Impact From Load

Uniform Load

Medium Impact

Strong impact

Uniform Load Motor Turbine

Hydraulic motor

1500 0,8 0,9 1 5000 0,9 1 1,25 27000 1 1,25 1,5 60000 1,25 1,5 1,75

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Light impact multi-cylinder

engine

1500 0,9 1 1,25 5000 1 1,25 1,5 27000 1,25 1,5 1,75 60000 1,5 1,75 2

Medium Impact Single

cylinder engine

1500 1 1,25 1,5 5000 1,25 1,5 1,75 27000 1,5 1,75 2 60000 1,75 2 2,25

Worm q value selection

The table below allows selection of q value which provides a reasonably efficient worm design. The recommended centre distance value "a" (mm)is listed for each q value against a range of z 2 (teeth number values). The table has been produced by reference to the relevant plot in BS 721 Example If the number of teeth on the gear is selected as 45 and the centre distance is 300 mm then a q value for the worm would be about 7.5 Important note: This table provides reasonable values for all worm speeds. However at worm speeds below 300 rpm a separate plot is provided in BS721 which produces more accurate q values. At these lower speeds the resulting q values are approximately 1.5 higher than the values from this table. The above example at less than 300rpm should be increased to about 9 Table for optimum q value selection

Number of Teeth On Worm Gear (z 2) q 20 25 30 35 40 45 50 55 60 65 70 75 80 6 150 250 380 520 700

6.5 100 150 250 350 480 660 7 70 110 170 250 350 470 620 700

7.5 50 80 120 180 240 330 420 550 670 8 25 50 80 120 180 230 300 380 470 570 700

8.5 28 90 130 130 180 220 280 350 420 500 600 700 9 40 70 100 130 170 220 280 330 400 450 520

9.5 25 50 70 100 120 150 200 230 300 350 400

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10 26 55 80 100 130 160 200 230 270 320 11 25 28 55 75 100 130 150 180 220 250 12 28 45 52 80 100 130 150 100 13 27 45 52 75 90 105

AGMA method of Designing Worm Gears

The AGMA method is provided here because it is relatively easy to use and convenient- AGMA is all imperial and so I have used conversion values so all calculations can be completed in metric units.. Good proportions indicate that for a centre to centre distance = C the mean worm dia d 1 is within the range Imperial (inches)

( C 0,875 / 3 ) ≤ d 1 ≤ ( C 0,875 / 1,6 )

Metric ( mm)

( C 0,875 / 2 ) ≤ d 1 ≤ ( C 0,875 / 1,07 )

The acceptable tangential load (W t) all

(W t) all = C s. d 20,8 .b a .C m .C v . (0,0132) (N)

The formula will result in a life of over 25000 hours with a case hardened alloy steel worm and a phosphor bronze wheel C s = Materials factor b a = Effective face width of gearwheel = actual face width. but not to exceed 0,67 . d 1 C m = Ratio factor C v = Velocity factor

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Modified Lewis equation for stress induced in worm gear teeth .

σ a = W t / ( p n. b a. y )(N)

W t = Worm gear tangential Force (N) y = 0,125 for a normal pressure angle α n = 20o

The friction force = W f

W f = f.W t / (. cos φ n ) (N)

γ = worm lead angle at mean diameter α n = normal pressure angle

The sliding velocity = V s

V s = π .n 1. d 1 / (60,000 )

d 1 = mean dia of worm (mm) n 1 = rotational speed of worm (revs/min)

The torque generated γ at the worm gear = M b (Nm)

T G = W t .d 1 / 2000

The required friction heat loss from the worm gearbox

H loss = P in ( 1 - η )

η = gear efficiency as above.

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C s values

C s = 270 + 0,0063(C )3... for C ≤ 76mm ....Else C s (Sand cast gears ) = 1000 for d 1 ≤ 64 mm ...else... 1860 - 477 log (d 1 ) C s (Chilled cast gears ) = 1000 for d 1 ≤ 200 mm ...else ... 2052 -456 log (d 1 ) C s (Centrifugally cast gears ) = 1000 for d 1 ≤ 635 mm ...else ... 1503 - 180 log (d 1 )

C m values NG = Number of teeth on worm gear. NW = Number of stards on worm gear. mG = gear ration = NG /NW

C v values

C v (V s > 3,56 m/s ) = 0,659 exp (-0,2167 V s ) C v (3,56 m/s ≤ V s < 15,24 m/s ) = 0,652 (V s)

-0,571 ) C v (V s > 15,24 m/s ) = 1,098.( V s )

-0,774 )

f values

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f (V s = 0) = 0,15 f (0 < V s ≤ 0,06 m/s ) = 0,124 exp (-2,234 ( V s )

0,645 f (V s > 0,06 m/s ) = 0,103 exp (-1,1855 ( V s ) )

0,450 ) +0,012

Working Drawing

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Conclusion: In the whole task we went through number of steps where we learnt the basic design parameters of grass cutting machine including their use and problems encountered by customers. Some how we could not complete our design project but even then we have an idea now that what basically the design is and what are the factors involving the design. We enjoyed working on it specially visited many places where this machine is installed and even at shops to get the data.