Traction Winch- Design, calculation and analyses P.F. CABRAL
Departamento de Engenharia Mecânica ISEL – ISEL – Instituto Instituto Superior de Engenharia de Lisboa Rua Conselheiro Emídio 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 on expedite 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 shipyard’s 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 Mecânico (Mechanical Project) subject s ubject as lectured le ctured in ISEL during the summer semester s emester of the 2012/2013 2 012/2013 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 s afe 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 15º inclined plan.
3. IDEATION
The author ’s ’s 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
P.F. Cabral 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 i deation 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: 15º
Inflatable rubber tire to concrete rolling friction coefficient: 0.035
Gravitational acceleration: 9.8 m/s² 3
P.F. Cabral
Load to be pulled: 10 t
As this: y
⃗
⃗ ⃗
x
⃗ 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 manufacturer’s 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, ¾ in wire rope with the following characteristics:
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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 rope’s cycling fatigue as per the manufacturer’s catalogue). The calculation process was as follows:
Knowing the drum’s 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 motor’s shaft:
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Consulting the chosen manufacturer’s catalogue [2] an electrical three phase induction motor with the following characteristics has been chosen:
Table 1- Siemens’s electrical 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 manufacturer’s [3] catalogue. Since the use of v-belt type transmission stages with ratios higher than 1:3 is not recommended the author has settled for that value for the traction winch’s 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 catalogue’s sizing method have resulted in a first transmission stage sized as follows: Input rpm Output rpm Ratio Type of belt Quantity of belts Belt section Primitive length Distance between shafts Driving pulley’s primitive diameter Driven pulley’s primitive diameter
3555 1128.6 1:3.15 V- belt 3 B 1800 644.6 100 315
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P.F. Cabral 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 teeth’s height, length and width as follows:
Solving for L and considering σ 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 stage’s driven pulley) will rotate 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:
teeth
This allows us to immediately determine the number of teeth for the driven wheel:
teeth
(16) 7
P.F. Cabral 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 gear’s 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 by Ft:
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 8
P.F. Cabral 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 gear’s teeth can result in an uncontrolled descent of the load, thus jeopardizing people and property, the author has implemented a safety factor of 2 to L:
Input rpm Output rpm Ratio Pressure angle Number of teeth z Module m Primitive diameter Dp Distance between shaft centers c Wheel width
Wheels 1,3 Wheels 2,4 Wheels 1,2 Wheels 3,4 Wheels 1,3 Wheels 2,4 Wheels 1,2 Wheels 3,4 Wheels 1,2 Wheels 3,4
1128.6 32 1:5.94 per stage 20º 17 101 7 7 119 707 413 100
Table 3- Second and third transmission stage’s 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 270º. The speed and torque considered were the same determined as fo r 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 friction coefficient):
Table 4- Screenshot of Shigley’s Mechanical Engineering Design table 16-3 regarding clutch and brake friction material’s characteristics.
Calculations for the acting loads follow:
φ
P1
P2
Image 6- Schematic of the loads acting upon the brake band
The maximum pressure that the friction material will suffer can be calculated by:
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This confirms the adequacy of the chosen friction material, which according to table 4 is able to 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 as follows:
Followed by the needed torque to apply this force:
The study of the tensions in the thread’s 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 rod’s collar and it’s 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 shaft’s free body diagram in the horizontal plane
Image 10- Primary shaft’s free body diagram in the vertical plane
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Image 11- Primary shaft’s 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 ration from 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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P.F. Cabral From here the combined bending moment can be calculated as a vectorial s um:
Having the author decided to manufacture the shafts from AISI 304 stainless steel with a yield strength and 215MPa and to implement a safety factor of 3, the Von Mises criteria can be applied as follows to determine a suitable shaft diameter:
As there the axial loads are negligible comes:
Thus a shaft with a diameter bigger than 30.2 mm is required to withstand the loads applied upon it. The dimensioning for fatigue has been developed from the following criteria:
As previously, the axial loads are negligible, so
Considering the following S-N curve for AISI 304 steel a value of 150 MPa for The correction factor have been set as follows:
Surface finish factor ks=0.78 (“as machined” surface finish);
Size factor kt=0.85 (diameter between 7.5 and 50mm)
is chosen.
Reliability factor kfb=0.702 (99.9% reliability is chosen as human or property damage can result from failure of this element)
Temperature factor kt =1 (temperature never exceeding 70ºC)
Fillet factor kf=1 (as the shaft is of constant section no fillets are required)
Also knowing that the ultimate strength for AISI 304 steel is 515 MPa the criteria can now be solved for d :
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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 of sizing 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 shaft’s own weight was calculated as follows:
Followed by the mid- beam deflection caused by the spur gear’s weight:
Solving Rayleigh’s equation for the first vibration mode comes:
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Dassault Systémes Solid Works 2012
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Since the primary shaft’s angular speed has already been determined to be of 1128.6 rpm the shaft 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 FAG’s proprietary online sizing tool. As previously mentioned, seal ed 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 winch’s own weight has been estimated to be around 1000kg with the mass properties resource of the used CAD system 2.
Image 15- Schematic of the forces acting upon the winch
2
Dassault Systémes Solid Works 2012
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P.F. Cabral The reactions at A and B supports have been found to be as follows under full load conditions:
Since there are 2 forward and two rear support points these loads need to be divided by 2 to found the values corresponding to each support point. The calculations for the forward supports is omitted because the rear set it that under more significant solicitation, not only due to the larger shear loads but also because the tractions loads observed tend to pull the winch away from the mounting plane. Calculating for the required pre-load to promote a friction force enough to overcome the shear condition returns:
Solving for the resulting traction effort (traction imposed by the load + pre load) on the rear sets of bolts:
Admitting the use of A2-70 stainless steel bolts with a proof strength for metric series of and implementing a safety factor of 10, given the risks associated with the failure of these components and also due to the fact that bolt oversizing translates into little additional cost in such project comes:
Being 33mm the minimum diameter if only one bolt were to be used in each support. Since this is a relatively high diameter, not promptly available, the author has decided to implement 4 bolts in each support. In this case the diameter of each one decreases as below determined:
Finally the following empirical expression was applied as suggested by Shigley’s Mechanical Engineering Design to determine the torque to be applied while tightening the bolts in order to bring them to the project pre-load:
Admiting k=0.2 comes:
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P.F. Cabral 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 Electrical, three phase (380V, 40.5A) Drive 10t Nominal load Rubber tire dolly over concrete Load support 15º Nominal slope 0.4995m/s Traction speed @ full load 50m Range Band type acting at the rolling drum shaft. Manually operated. Brake
Table 5- Winch’s characteristics
Component Steel rope Motor Belts Driving pulley Driven pulley Primary shaft Secondary shaft Drum shaft Spur gears 1, 3 Spur gears 2,4 Primary shaft’s bearings Secondary shaft’s bearings Drum shaft’s bearings Brake threaded rod Brake’s friction material Fixing bolts
Characteristics AISI304, 6x19 22kW, 3555rpm V type, Section B, L=1800 100mm, 3slots,secção B 315mm, 3slots secção B AISI304, Ø40x1490 AISI304, Ø70x1405 AISI304, Ø120x1405 AISI410, z=17, Dp=119, L=100 AISI410, z=101, Dp=707, L=100
80x40x23, sealed self aligning ball bearings 125x70x31, sealed self aligning ball bearings 215x120x42, sealed self aligning ball bearings Square thread, 5x5, d=28, AISI410 Cinta 10x100 woven asbestos yarn and wire M18 A2-70
Qty 50m 1 3 1 1 1 1 1 2 2 2 2 2 1 1.65m 16
Table 6- Winch’s 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 15º used as a reference for the sizing process:
5. FINITE ELEMENT ANALYSES
Dassault systémes 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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P.F. Cabral Support type
Bearing suport
Considered loads Gravity
Gearing force
Type Gravity Applied along a split line drawn longitudinally across a tooth at primitive diameter’s height. Room temperature
Value 9.8m/s²
18246N
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 Lewis’s equation’s 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 component’s 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.
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