winch analysis

8/11/2019 Winch Analysis

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Traction Winch- Design, calculation and analyses

P.F. CABRAL

Departamento de Engenharia Mecnica

ISELInstituto Superior de Engenharia de Lisboa

Rua Conselheiro Emdio Navarro, 1- 1959-007 Lisboa

Email: [email protected], web:http://www.otrimaran.blogspot.com

Keywords: Mechanical engineering design, traction winch, finite element analyses, traction

winch

Abstract This paper describes the ideation, design, conventional sizing calculation based onexpedite empirical equations and validation of the results by the use of finite elements

analyses of the critical components in a traction winch intended for use in marine

environment, such as those often found in shipyards slipways, leisure marinas and sailing or

boating clubs to winch boats out of the water. It transcribes and resumes the essence of the

project developed by the author for final evaluation at the Projecto Mecnico (Mechanical

Project) subject as lectured in ISEL during the summer semester of the 2012/2013 academic

period.

1. INTRODUCTION

Traction winches can be found in marinas, shipyards, boating clubs and generally wherever a

boat slipway is found all over the world. Their purpose is to provide a reliable and safe means

of pulling boats over wheeled dollies out of the water up an inclined plan, being found in

many sizes and pulling capacities adequate for the maneuver of all kinds of vessels from the

smallest leisure yacht to the largest ocean freighter.

2. GENERAL SPECIFICATIONS

The traction winch hereinafter described shall have the following characteristics and

performance:

Suitable for long, maintenance free operation in marine environment;

Electrically driven;

Equipped with an adjustable brake;

Capable of a nominal traction speed of 0.5m/s at full load;

50m range;

Maximum pulling capacity of a 10t load over inflatable tires in a 15 inclined plan.

3. IDEATION

The authors experience in boating has contributed for the initial empirical ideation of the

mechanism. It has been observed that the rugged construction and apparent over-sizing
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normally associated with these equipments is needed to allow sustained safe operation and

reliability even under the harsh corrosive seaside environment and occasional overloads

imposed by careless operation such as the use of dollies with poorly inflated tires or badly

corroded bearings, unintentional inversion of the traction direction while lowering boats to the

water, operator disregard for the capacity of the machine, namely in what concerns maximum

pulling capacity, lack of or poor maintenance. In this regard the initial ideation has produced

the mechanism described as follows:

Electrical motor with high start-up torque, allowing for the winch to resume pulling

even if the load is for some reason brought to a halt while still in the inclined plan;

Multiple transmission stages after the and use of a high speed electrical drive motor to

allow for the use of as small a motor as possible, while keeping the considerations of

the previous point;

First transmission stage achieved with v-belts, thus allowing for smooth start-up and,

most importantly slippage if the maximum load is grossly exceeded; Spur geared second and following transmission stages for maximum torque

transmission capability and system reliability;

Shafts, chassis, drums, gears, traction steel rope and accessories built of stainless-steel

alloys whenever possible;

Use of sealed, pre-lubricated bearings from a well regarded brand to keep the

maintenance intervals as far apart as possible;

Use of self-aligning bearings to allow for minor misalignments of parts during

installation and bending of shafts under effort while at load without imposing untimely

wear to the bearings; Service brake coupled to the shaft of the steel-rope drum, thus allowing the operator to

maintain full braking capacity even after catastrophic failure of any of the

transmission stages (including belt breakage at the first stage);

Hand operated service brake of uncomplicated and reliable conception so that the

braking capacity is kept even after electrical failure

These considerations together with observation of similar mechanisms already in service have

allowed the author to proceed with an initial 3D modeling idealization of the traction winch as

follows:


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Image 1- Overall view of the traction winch, as initially idealized (full-scale human figure provided for scale

perception)

Image 2- Idealization of the drive train/brake assembly

4. SIZING

The sizing of all the components of the project has been developed from the effective traction

load imposed by the following conditions:

Inclined plan slope: 15

Inflatable rubber tire to concrete rolling friction coefficient: 0.035 Gravitational acceleration: 9.8 m/s


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Load to be pulled: 10 t

As this:

Image 3- Actuating force diagram

{ {

Applying a 50% safety factor to allow for misuse and overload comes: 4.1.Steel rope sizing

The steel rope has been sized following the recommendations of the manufacturers technical

catalogue [1], which also provides guidelines for the sizing of the drum.

Having followed the mentioned catalogue the author settled for an AISI304 (UNS S304000)

stainless steel 6x19, in wire rope with the following characteristics:

y

x


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Image 4- CERTEX catalogue screen capture showing the characteristics for the different sizes of the chosen steel

wire rope

From the required range for the winch it was also possible to calculate the needed number of

turns around the rolling drum and, consequently, the width of the drum that will dictate the

overall width of the winch. Note that the author as predicted the use of a non-overlapping

rolling drum:

As 50 meters of cable are needed and the perimeter of the 300mm drum is 0.942m:

Considering that each turn of cable is rolled around the drum with no gap to the previous: (4)4.2.Motor sizing

The torque needed at the rolling drum shaft has been determined knowing the pull at the rope

and the diameter of the drum, which has been established at 300mm (an acceptable value in

terms of the ropes cycling fatigue as per the manufacturers catalogue). The calculation

process was as follows:

Knowing the drums diameter(300 mm) and the required traction speed (0.5 m/s) it has also

been possible to calculate the angular speed required at the drum shaft:

Assuming the use of a 3600 rpm motor the total transmission ratio could be calculated as

follows:

This value, applied to the previously determined required torque at the drum shaft has allowed

the author to determine the required torque at the motors shaft:


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Consulting the chosen manufacturers catalogue[2] an electrical three phase induction motor

with the following characteristics has been chosen:

Table 1- Siemensselectrical motors catalogue screenshot with the selected model highlighted

Since the effective rpm of the chosen unit is 3555, not 3600 as previously considered, the

already determined values had to be fine tuned as below:

4.3. Drive train sizing- first stage

As previously mentioned, the first transmission stage is one of v-belt typology which has been

calculated by means of the comprehensive method proposed by the chosen manufacturers [3]

catalogue. Since the use of v-belt type transmission stages with ratios higher than 1:3 is notrecommended the author has settled for that value for the traction winchs first transmission

stage. The use of pulleys with primitive diameter smaller than 100 mm is also not advisable.

As such and taking into account the use of standard diameters the author has opted for a

transmission stage composed by a driving pulley with a primitive diameter of 100 mm and a

driven one of 315 mm. This conducts to an effective transmission ratio of 3.15 which results

in an output rpm of:

All the previous considerations applied to the catalogues sizing method have resulted in afirst transmission stage sized as follows:

Input rpm 3555

Output rpm 1128.6

Ratio 1:3.15

Type of belt V- belt

Quantity of belts 3

Belt section B

Primitive length 1800

Distance between shafts 644.6

Driving pulleys primitive diameter 100Driven pulleys primitive diameter 315


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Table 2- First transmission stage main characteristics

4.4.Drive train sizing- second and third stages

The second and third drive train stages are composed by spur gears coupled to their shafts

with adequately sized parallel keys. The gears have been dimensioned following the method

proposed by the reference literature [4], namely the Lewis equation which equates the

bending tension acting on any tooth in a given spur gear in terms of the tangential force, the

gear teeths height, length and width as follows:

Solving for L and considering as the allowable tension for the selected material leaves us

with an expedite mean of determining the length of the teeth, which corresponds to the width

of the geared wheel: As a starting point the author has chosen a module of 7 for the gears to be used and has

divided the reduction needs remaining from the first stage in equal parts for the second and

third stages, thus simplifying the project by means of using sets of similar gears. It was also

taken into account the recommendation of the reference literature that gear reductions shall

not be higher than 1:10 per stage. The calculations were developed as follows:

It is known that the primary shaft (coupled to the first transmission stages driven pulley) willrotate at 1128.6 rpm. It is also known that the needed rpm for the drum shaft is 32 rpm. This

allows us to establish that the combined reduction of the second and third stages must be:

As previously mentioned it has been decided that the second and third stages will feature

equal ratios. This can be calculated by:

To avoid teeth interference the following equation [4] allows one to determine the minimum

number of teeth in any given gear train as a function of its module and angle of pressure:

Making k=1 (coefficient for spur gears) comes:

( ) teethThis allows us to immediately determine the number of teeth for the driven wheel:

teeth (16)


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Widely know formulae allow the development of several simple calculations to determine the

remaining unknowns for the Lewis equation:

Teeth height:

; ; Teeth width:

; ; ; Tangential force:

Image 5- Schematic of the forces acting upon spur gears teeth

Taking into account that all wheels must have the same module, construction material and

width the author has simplified the calculations by developing these for the worst case

scenario which is the last gear of the mechanism.

It is known from previous calculations that the torque at the drum shaft is:

Also knowing that the primitive radius of the bigger gears is:

707/2=353.5

Fn can now be determined:

Followed byFt:

The author as opted for the use of AISI 410 cast stainless steel allow for the construction of

the gears. This material, while presenting reasonable mechanical characteristics and very good


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corrosion resistance also allows surface hardening by nitriding, which makes it adequate for

gear building. The yield tension for this material is 276 MPa.

The Lewis equation can now finally be applied and the teeth length determined as follows:

Since the catastrophic failure of the last gears teeth can result in an uncontrolled descent of

the load, thus jeopardizing people and property, the author has implemented a safety factor of

2 toL:

Input rpm 1128.6

Output rpm 32Ratio 1:5.94 per stage

Pressure angle 20

Number of teethzWheels 1,3 17

Wheels 2,4 101

Module mWheels 1,2 7

Wheels 3,4 7

Primitive diameterDpWheels 1,3 119

Wheels 2,4 707

Distance between shaft centers cWheels 1,2Wheels 3,4

413

Wheel width Wheels 1,2Wheels 3,4

100

Table 3- Second and third transmission stages characteristics

4.5.Brake

The author as decided for a simple band brake acting upon a drum coupled to the last shaft of

the transmission. The brake is to be manually operated through a crank wheel coupled to a

threaded rod that will tighten or loosen the band against the drum.

The sizing method for the apparatus was that suggested by the reference literature [4]

The diameter of the brake drum and the hugging angle of the band have been set respectively

at 700mm and 270.

The speed and torque considered were the same determined as for winching up.

To choose an adequate friction material the linear speed at the contact surface must be

determined:


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From the following table an adequate material is chosen based upon the previously calculated

speed, the choice of the highest friction coefficient and on the assumption that the brake will

be of the dry type (this excludes resilient paper material with an even higher frictioncoefficient):

Table 4- Screenshot of Shigleys Mechanical Engineering Design table 16-3 regarding clutch and brake friction

materials characteristics.

Calculations for the acting loads follow:

Image 6- Schematic of the loads acting upon the brake band

The maximum pressure that the friction material will suffer can be calculated by:

P1 P2


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This confirms the adequacy of the chosen friction material, which according to table 4 is ableto withstand pressures as high as 100 psi.

The sizing of the threaded rod has been developed as follows, based as well on the

methodology proposed by the reference literature [4].

Condition for the thread system to be self-locking under load:

Considering a coefficient of friction of 0.15 (typical for dry steel to steel interaction) the

thread helix angle can be calculated as follows:

Considering a 28mm threaded rod with a 5 x 5 square section thread the pitch can now be

determined:

The force needed to apply the needed braking effort to the system can be determined asfollows:

Followed by the needed torque to apply this force:

The study of the tensions in the threads fillets can now be developed:


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Image 7- Schematic of a square section thread fillet

The following equations have been solved, as suggested in the reference literature [4], to

determine if the thread (machined from AISI 410 stainless steel rod with 276MPa yield

strength) is able to withstand the loads imposed upon it:

This confirms the adequacy of the chosen material and section.

To finalize the dimensioning of the brake system remains the calculation of the force that an

operator needs to exert in the crank wheel to actuate the brake at full braking capacity. To do

so it is needed to calculate torque resulting from the friction between the threaded rods collar

and its mounting:

Admitting a collar with a 60mm diameter, a 0.15 coefficient of friction and considering the

previously calculated 3700N force comes:

The total force to exert by the operated can now be calculated as follows, admitting a crank

wheel with a 218mm radius:

This is considered an acceptable value for an average adult to be able to apply effortlessly.


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Image 8- Detail rendering of the brake system

4.6.Shafts

The three transmission shafts of the winch have dimensioned taking into account all the loads

applied to them, including their own weight due to their relatively high diameter to length

ratio. The calculations have been developed in terms of yield strength, fatigue and resonance

as below described for the primary shaft (for the remaining two the same procedure was

used). The used method was that suggested by the complementary reference literature [5]:

Image 9- Primary shafts free body diagram in the horizontal plane

Image 10- Primary shaftsfree body diagram in the vertical plane


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Image 11- Primary shafts applied torsion distribution diagram

RA, RB: Reactions at the supports

FC: Load due to the forces exerted by the belts

FR: Load due to the forces exerted by the gears

M: Applied torsion

Knowing the needed torque at the last shaft and also knowing that the transmission rationfrom there to the primary shaft is 1:111.4 the applied torsion at this shaft can be determined

as:

All the applied forces in the previously drawn free body diagram were equated in force

equilibrium equations which resulted in the following bending moment diagrams:

Image 12- Bending moment in the horizontal plane

Image 13- Bending moment in the vertical plane


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( ) Meaning that the previous sizing for yield strength of 30.2 mm still prevails.

The dimensioning against the occurrence of resonance was developed under a principle ofsizing the shaft in such way that the first vibration mode is never achieved under operation.

These calculations have been developed as follows:

The 30mm shaft has been reduced to two mass-spring systems, one regarding the part

between supports and another regarding the overhanging part where the v-belt pulley is

coupled:

Image 14- Schematic of the considered mass-spring systems

The first calculation was performed with reference to the longest beam since this is the worse

case scenario for this system:

The mass of the part of the shaft confined between the supports has been calculated:

The mass of the spur gear has also been determined with the mass properties resource of the

CAD system used 1:

The mid-beam deflection caused by the shafts own weight was calculated as follows:

Followed by the mid-beam deflection caused by the spur gears weight:

Solving Rayleighs equation for the first vibration mode comes:

1Dassault Systmes Solid Works 2012


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Since the primary shafts angular speed has already been determined to be of 1128.6 rpm theshaft is found to be oversized by ~25%. However the author has decided to perform one more

iteration since, due to the high gear ratio, small variations in the load speed, namely while

descending, can easily cause the primary shaft to achieve critical speed. Solving the previous

method for a 40mm shaft returns an acceptable oversizing allowing the shaft to turn safely

bellow its first mode vibration at up to approximately 31000 rpm.

Parallel keys have been sized by simple shear resistance calculations. Adequate DIN 6885

types have been chosen for all shafts.

4.7.Bearings

Bearings have been chosen for the determined loads, angular speeds and shaft sizes using

FAGs proprietary online sizing tool. As previously mentioned, sealed self aligning types

have been chosen in order to absorb the bending of the shafts without imposing the damaging

loads that would result from the use of cheaper non self-aligning components. The mounting

of the bearings is achieved by use of circlips.

4.8.Fixtures

The winch is to be fixed to its anchoring with stainless steel machine bolts. As the resulting

loads at these bolts is expect to be of the shear type, pre loading of the bolts is required to

eliminate its adverse effects. The calculation methods used follows:

The winchs own weight has been estimated to be around 1000kg with the mass properties

resource of the used CAD system2.

Image 15- Schematic of the forces acting upon the winch

2Dassault Systmes Solid Works 2012


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4.9.COMPILATION OF THE RESULTS

The previous calculations have returned the following table which resumes the main

characteristics of the traction winch as well as those of its most important mechanical

components:

ELECTRICAL TRACTION WINCH FOR MARINE ENVIRONMENT OPERATION

Drive Electrical, three phase (380V, 40.5A)

Nominal load 10t

Load support Rubber tire dolly over concrete

Nominal slope 15

Traction speed @ full load 0.4995m/s

Range 50m

Brake Band type acting at the rolling drum shaft. Manually operated.

Table 5- Winchs characteristics

Component Characteristics Qty

Steel rope AISI304, 6x19 50m

Motor 22kW, 3555rpm 1

Belts V type, Section B, L=1800 3

Driving pulley 100mm, 3slots,seco B 1

Driven pulley 315mm, 3slots seco B 1

Primary shaft AISI304, 40x1490 1

Secondary shaft AISI304, 70x1405 1

Drum shaft AISI304, 120x1405 1

Spur gears 1, 3 AISI410, z=17, Dp=119, L=100 2

Spur gears 2,4 AISI410, z=101, Dp=707, L=100 2

Primary shafts bearings 80x40x23, sealed self aligning ball bearings 2

Secondary shafts bearings 125x70x31, sealed self aligning ball bearings 2Drum shafts bearings 215x120x42,sealed self aligning ball bearings 2

Brake threaded rod Square thread, 5x5, d=28, AISI410 1

Brakes friction material Cinta 10x100 woven asbestos yarn and wire 1.65m

Fixing bolts M18 A2-70 16

Table 6- Winchs main components

It as also been possible to deduce na equation to calculate the maximum weight of the load to

be pulled as a function of the slope, shall the winch be used in an inclined plane with a slope

diferent of the 15 used as a reference for the sizing process: 5. FINITE ELEMENT ANALYSES

Dassault systmes Solid Works Simulation module has been used with the objective of

compare its findings with the analytical results. The following paragraphs present the study

performed upon the dimensioning of the more severely solicited spur gear while under full

service load:


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Support type Considered loads Type Value

Bearing suport

Gravity Gravity 9.8m/s

Gearing forceApplied along a split line drawn longitudinallyacross a tooth at primitive diameters height.

18246N

Room temperature

Table 7- Simulation conditions for spur geared wheel number 4

Images 16 and 17- Simulation fixtures and loads

Image 18- Finite element mesh


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Image 19- Maximum simulated Von Mises stress

A maximum Von Mises strees of 90.31 has been observed as the result of the simulation. This

corresponds to a factor of safety of safety of around 3, a results that classifies Lewiss

equations numbers as conservative.

6. CONCLUSIONS

From the development of this paper, and of the complete report on which it is based, the

author has been able to conclude the following:

The process of conception and calculation of mechanical systems is one of heavily

iterative nature, experience being a very important factor in allowing the engineer to

approach the design with empirical initial sizings close to those that calculations will

confirm to be the final components characteristics, thus savig precious design time;

The sizing equation used to dimension the spur gears (Lewis equation) is fairly

conservative by comparison with the finite element analyses results. This illustrates

the principle that shall govern every engineering project and by wich the designer

must always be suspicious of the results obtained by a single methodology, being a

good principle and practice to always confirm results by means alternative to those

used in the first place, especially if major personell or property damage is probable of

resulting from failure of the designed equipment.

winch analysis

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