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Steps in Design of a Hoisting System

©Dr. B. C. Paul 1999 major revision 2012

With Credit to Dr. H. Sevim for Original Book

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Steps in Design of Hoisting System Determine the performance requirements

• Usually means production• can also involve figuring acceptable stopping

distances - number of levels to be served under what conditions

Select hoist type to meet constraints

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Once Upon a Mine

Dark Black coal mine will produce 3 million tons of coal from a single level. The hoisting distance from loading pocket to dump bin is 1000 ft. The mine operates 250 days per year 3 production shifts per day with 7 hours of operation each production shift. The peak production will be about 5000 tons per shift. The average production is 4000 tons per shift.

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Your Mission Jim, Should you decide to accept it Design a hoisting system for the Dark Black Coal

Mine.

First Step is to establish the performance requirement.

The fundamental Capacity Equation is• Q = P / T• Q is requirement in Tons Per Hour• P is Production per shift• T is the average shift production time

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Which Production Number Do We Use? Actual production is a distribution - not an

average number If we design on average then all the

numbers above the mean will go past capacity - we’ll loose our high values and not meet production

If we design on a peak that is seldom achieved we’ll pay big bucks

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Decision Criteria

If peak approaches 2 times average - need to consider cost of work stoppage vs. take work stoppages

If peak is somewhat close to average then design for the peak

In example the peak is 125% of the average, which is not considered a significant deviation. Design for the Peak!

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What if Life had not been so Kind? Calculate the cost of a production stoppage

• May be cost of lost production• May include penalties on contracts• May include idle labor cost

Calculate the amortized cost of the next increment of production capacity

Check multiple points and go for minimum total cost.

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Pick production capacity Apply formula

• 714 tph = 5000 t/shift / 7 hours prod time

Other design decisions need to be made• Is this a Keope or a Drum Hoist?• One Level so Keope won’t be too tricky

Input My Hoist Distance and Production Rate Target

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My Spreadsheet isOpti-Hoist.

Next Lets look at some fixedCycle time elements

Elements

How Long will it take for the ore pocket doors to open and drop a load into the skip?

Once the Skip is in position how long will it take to deposit the load into the dump point chute?• About 8 seconds to load• 10 seconds to dump is reasonable• Your load and unload times may depend on other

design elements of the system.10

Creep Time

Hoists and Elevators slow to near stop as they line up with a set level• Pull away fromthe loading point

• Or line up with dump point

• Will Usually take a bit more time to line up with the unload point

• 2 seconds to pull away from load and 4 to line up with dump is reasonable.

11A fowl Beast

Now We Need to Pick a Peak Speed and a Rate of Skip Acceleration

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The maximum speed we lift at is safety related. For men there are regulations.For materials there are guidelines (shown in pink)

Considerations

This is a Keope Hoist• The rope is just sitting over a friction wheel• If I “peel out” and the rope starts to slip I have

a major hoisting accident

High speed and high acceleration increase production• But they also cause a big increase in motor size

and energy bill.

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I’m going to go for modest speed and particularly modest acceleration

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Geometry Considerations

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Two Skips Skip and Counter-weight

Stopping Considerations

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If my controls missStopping the skip atThe dump point – howFar do I have for anEmergency stop beforeThe over-wiend turnsInto a disaster?

DumpChute

Loading chute

Shaft Bottom

Getting Our First Estimate

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Using a Nordberg approximation of the cycle time the program estimates the sizeOf skip that will be needed to achieve the production target using the distance,Speed and acceleration conditions specified.(This part of the spreadsheet is independent of whether the hoist was a Keope orA drum hoist).

Our Next Task is to Get Our Exact Cycle Time

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The only missingPiece of informationWas what is theCreep speed (2 ft/secIs reasonable).

(I want’s you money for my fakeGlobal warming initiative)

Next We Must Balance Skip Size, Weight, Rope Diameters and Wheel Sizes

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First We Need to Pick A Skip Size

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We have already been given a first guess skip size. We try about that sizeAnd then check the actual hourly production achievable in the red box (weNow have figured the exact cycle time too).

As can be seen a 16 ton skip will get me my 720 tons/hour.

Next I’ll Go for Skip Weight

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In general a skip heavy enough to handle the banging of ore loading andUnloading will weight about 75% of the load weight.

Opti-Hoist estimates this for us but leaves us a yellow blank to choose theWeight. A higher weight usually means we are just adding weights to ourSkip.

Next We Go For Rope Sizing

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Keope hoists usually have multiple ropes in even numbers, 2, 4, 6, and 8 beingCommon. Where that 12 came from is unsure.

We need to consider both hoisting ropes and tail ropes. Sometimes tail ropesAre used and worn-out hoist ropes which can cause tail ropes to be the sameAs hoist ropes.

My First Guess is 4 ropes(This is a relatively modest depth)

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The red box estimates that I will need a 1.064 inch rope to reach neededSafety factors for this depth.

From Here I Need to Go And Enter My Rope Properties

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I enter my rope size, it’s weight and it’s strength. (I have the advantage ofHaving an estimate of what size rope to try).

The spreadsheet then compares the achieved factor of safety to what is required

Where Do I Get These Rope Properties

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The spreadsheet has aRope properties tableRight below for me toLook things up on.

I’m looking for 1.064Flattened strand

I go for 1.125Weight 2.28 lbs/ftStrength 57.9 tons

Enter My Rope and Check My Factor of Safety

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A 7 factor of safety clearly meets a 6.5

I Wonder If I Could Get Away with a 1 inch rope

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Eeee – one inch rope is a nope.

What if I Use High Strength Steal?

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Oh so close but still nope to the rope

With Hoist Rope Selected I can now pick the Wheel for My Hoist Frame

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I need a 7.5 ft wheel (see pick recommendation) to avoid bending my rope toSharp. (You can see why I wanted a smaller rope – it would have allowed meTo use a smaller lower inertia wheel).

Now I Need to Deal with Tail Rope Simple case is to get used rope Also easiest to have just one tail rope so

have less swinging and tangling. Number of tail ropes is commonly less than

number of hoist ropes.

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I’m going to try straight across Using my worn-out hoist ropes for tail ropes.

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Now I’ll Check Conditions at My Keope Wheel

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T1 is the weight of the heavy loaded side. T2 is the weight of the lighter emptySide.

Remember – only friction stops the rope from slipping. The ratio of T1 to T2Must therefor not be more than 1.5

Of course 1.95 is greater than 1.5 so life is sucking right now.

Another Parameter is Tread Pressure

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Keope wheels are normally lined with a leather like frictional material. Since weDon’t want the ropes to cut the material to pieces we need to limit the load toAbout 300 psi or less.

Well at least one thing worked.

So What Do I Do Now

Either T1 is to big or T2 is too little I could look at rope weight but the rope weight

shifts back and forth from T1 to T2 depending on where we are• The T1 and T2 ratios are picked by the spreadsheet to

be worst case

I could make my skip lighter• But a light duty skip could get beat to pieces• And a lighter skip would also reduce T2

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Idea

If my skips were heavier then the skips would account for a higher percentage of the weight.

Since skips are the for T1 and T2 making it a larger proportion will even the ratio

(I could make a similar argument for picking heavier ropes but ropes are expensive and big ropes for larger higher inertia wheels).

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Putting 8 tons of Dead Weight on My skips made it more even

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Of course I’m still not there yet.

Ok – Adding 15.5 dead weight tons to the skip did it!!!

37Oh boy did it do it – take a look at that tread pressure.

So What Can I Do With My Tread Pressure I can’t change my T1 and T2 But I can spread the load over a greater area

• That unfortunately would mean getting a bigger Keope wheel

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There – A 10 ft Wheel Spreads the Load

39I know – the inertia situation sucks.

Come to Think About It – The Factor of Safety Sucks Too

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How profound – I put more weight on the rope without strengthening the ropeAnd I get into safety factor trouble.

(Where theMoney Goes)

Take A Little Weight Off the Skip and Put A Little More On the Rope

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Time to Pick Out Our Motor

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Looking at Hoist Duty Cycle

Hoist doesn’t always run at a single speed Initial acceleration - time it starts to move -

but its by the loading pocket so we don’t “floor it”

Creep 1 - carefully creeps past the loading area to avoid tearing something up

Main acceleration - after clear of loading area - hit it up to full speed

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Hoist Duty Cycle

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Duty Cycle Continued

Run at Full Speed - until you get close enough to the top that you’d better slow down or you'll put the skip up someplace interesting

Main Deceleration - slow down to creep speed before you take out the dump bin

Creep 2 - move slowly into dump position Final Deceleration - stop to dump

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What Size Motor?

Required horsepower for motor varies greatly through hoisting cycle

Adjustments are made by calculating the Root Mean Squared (RMS) Horsepower requirements

This requires taking horsepower duties at multiple points through the hoisting cycle

The Spreadsheet Does Your Calculations

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The Motor Sizing isA function of somethingCalled EEW – what isthat.?

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The Mystery of the EEW Term EEW stands for equivalent effective weight Hoist contains motors, gears, and large

wheels that contribute inertia to the system during acceleration

Could go through long hand and calculate inertia of everything (if you’re sadistic enough)

Alternative is to use manufactures tables that reduce inertia to an equivalent load on a rope.

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Nordberg Equivalent Effective Weight Chart

Reading the Chart

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We know it isA Keope hoistSo I will useThe Keope line.

I know I haveA 10ft wheel

So I start at10 and read upTo the KeopeLine

I Then Read Over to the Equivalent Effective Weight

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I’ll be conservativeIn my reading andCall it 36,000 lbs

Enter the Number and Get MotorSizing

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Of course understandingWhat all these HP1, HPAAnd TSL stuff is wouldAdd a lot of understanding

Keope Hoist 53

The Horsepower Demand of a Keope Hoist Over Time Looks Like This

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Understanding Keope Duty Cycles

Q - Why is there a steady flat line for Horsepower required in a Keope Hoist Duty Cycle

A - Horsepower is an energy output per unit time. It takes energy to lift the skip load up the shaft as it travels at full steady speed.

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Keope Duty CyclesQ - Why is there a sloped line leading upward from when the hoist starts

A - When the hoist is operating at less than full speed the load is transported a lesser distance per unit time and thus the energy output per unit time is less. The line has a linear slope because the acceleration rate is a constant.

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The Keope Duty CycleQ - Why is there a peak that drops sharply to the flat line for Horsepower to run the Keope

A - You must add additional force to accelerate the load. At the end of the acceleration period the additional force is no longer needed.

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Keope Duty CyclesQ - Why is there a big drop in horsepower at the end of the full speed run for the hoist

A - When the hoist decelerates, the momentum of the load provides part of the energy to keep the load moving up the shaft.

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Keope CyclesQ - Why does the line slope down at the end of the Hoist Cycle

A - The load is slowing down and accumulating less potential energy per unit of time.

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Keope CyclesQ- Why the funny dashed lines that show more power being used at the start and less being recovered at the end.

A - Frictional losses

Keope Hoist 60

Approach to Attacking the RMS Horsepower Requirements We will calculate components of Horsepower

requirements• HP1 will be the horsepower to accelerate the load

• HP3 will be the horsepower to move the load at full speed up the shaft

• HP2 will be the horsepower recovered from momentum when the load is decelerated

• HP6 will be the horsepower still required to lift the load after deceleration starts

• HP4 and HP5 will cover frictional losses

You Can See Those Horsepowers Calculated.

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Keope Hoist 62

Horsepower #1 (For Keope Hoists) HP1 = TSL * V2 / (550 * g * Ta)

• Where TSL is the Total Suspended Load• V is the Velocity• g is the acceleration of gravity• Ta is the acceleration time to get the hoist to full

speed and includes time to accelerate to creep speed (initial acceleration t1) and then to accelerate to full speed (t3)

• Ta = t1 + t3

Keope Hoist 63

Total Suspended Load TSL = EEW + 2000 * SL + 2*(2000*SW)

+ Rope Weight (both sides)• SL and SW are the skip weight and load in tons• R is the rope weight

• Because of tail rope there is a full length of rope on both skip sides

Keope Hoist 64

Horsepower #3 - Power to Lift a Loaded Skip at Full Speed HP3 = V * 2000 * SL / 550

• Note that the skip weight term is missing• I have a skip going down to balance a skip

coming up

Keope Hoist 65

Horsepower #2 - Negative Horsepower from Momentum During Deceleration HP2 = - TSL * V2 / (550 * g * Tr)

• Where Tr is time during deceleration

Keope Hoist 66

Horsepower #4 - Losses in Gears and Drives Derived empirically rather than by physics

fundamentals HP4 = 0.111 * (2000 * SL * V / 550)

Keope Hoist 67

Approach to RMS Horsepower Continued We will add the different fundamental components

of horsepower to get the horsepower needs at various cardinal points during the lift

We will label these cardinal points A through E• Example D is the peak power required at the height of

the acceleration phase

We will put the horsepower values at the cardinal points into the RMS horsepower equation and use that to size the motor.

Keope Hoist 68

Calculate Horsepower at 3 Cardinal Points Point A - Peak of the Acceleration Phase HPA = HP1 + HP3 + HP4

Point B - During Full Speed Run HPB = HP3 + HP4

Point C - At Initiation of Deceleration HPC = HP2 + HP3 + HP4

Yip – There are the values

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Keope Hoist 70

One More Monster Power Sink

These Big Motors have an Armature to Sink a Battleship! - takes a lot of inertia to spin the thing up or down

HP5 (to spin it up) = 0.75 * HPA * 1.2 / Ta

HP6 (to spin down) = -0.75 * HPA * 1.2 / Tr

Those Calculations are Done Too

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Keope Hoist 72

Correcting Cardinal Points for Armature Acceleration Point D is the revision of A peak of

acceleration HPD = HPA + HP5

Point E is revision of C initiation of Deceleration

HPE = HPC + HP6

And the Calculations Are There

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Keope Hoist 74

RMS Equations Depend on Motor Type For AC Motor HPrms = [ ( HPD

2 * Ta + HPB2* Tfs + HPE

2* Tr)/ ( 0.5 * Ta + Tsf + 0.5 * Tr + 0.25 * tr) ]0.5

• Where • Ta is acceleration time

• Tsf is full speed time

• Tr is deceleration time

• tr is the rest time

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RMS Horsepower for DC Motors

Numerator is the same as AC Denominator is changed to ( 0.75 * Ta + Tsf + 0.75 * Tr + 0.5 *tr)

RMS HP DC = [ Numerator/ Denominator]0.5

Looks Like I Need About 1200 HP

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Time to Pick the Motors

77I need to choose the number and size of motor and the inertia of the rotor

Consider Picks

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I’d rather go AC with frequency control. I’d like to do 2 600 hp motors butWith a 10 ft diameter Keope wheel I’ll still need gear reduction so I wouldOnly get about 94% transmission – My pick a 1250 two pole AC

Plug-In My Motor Parameters and Gear Reduction Efficiency

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Ok – That seems to work(Note that there are limits to how much you can turn down the speed ofA motor with variable frequency drives)

Our Last Task is to Size the Brake

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We Want Two Things From Our Brake Hold the maximum possible ubalanced load

with a 1.5 factor of safety If a full speed load passes the ore dump

speed it must perform an emergency stop before the skip crashes into the top of the headframe.

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Next Step is to Design the Braking System During Clutching Operations the Brake must hold the

load so it doesn't go to the shaft bottom Design practice is to rate the brake and clutch to hold

the maximum load plus 50% BR = CR = (D/2) * ( 2000*SL + 2000*SW + H * Wr *

n) * (1.5) {Units are ft-lbs}• D is drum or wheel diameter• BR and CR are Brake and Clutch Ratings in ft*lbs torque • Note this is the load on one side of a drum hoist if the other is

clutched

The Spreadsheet Runs the Calculation

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I need to set my brake rating to at least this size.

I Fill In the Numbers

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Brake rating comes from the recommendationMass of the rotor came from the motor specification listThe gear ratio and speed were worked to get a workableRatio and a motor speed that was within the turn-downLimit for the motor.

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Another Factor is Brake Performance During an Emergency Stop Design is done on worst case scenario

• maximum unbalanced load traveling at full speed• discovered with a minimum tolerance distance

before you ride into the head frame or crash into the bottom

Must either design for a tolerance distance your brake can stop in or size up the brake for the tolerance you have.

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Design Concept Assume the Brake must fight against the

maximum unbalanced load• Subtract unbalanced load from brake capacity• This leaves the net force available for the

emergency stop Use Newtons Second Law

• Know the net force available• Know total mass in motion• Solve for the deceleration rate

Calculate the time and distance to stop

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Formula

Look at Maximum differential load• W = (T1 - T2) * 2000

• T1 = Max load = SL + SW + (H * Wr * n/2000)

• T2 = Min Balancing Load = SW

The Spreadsheet Applies the Formula to Get the Differential Weight.

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The Mass that must be Stopped

To use Newton's Law to get Force Requirements the load must be in mass• Means we must use slugs - some how a system made by Kings using slugs

sounds wrong

M = [ ( EEW * R2 + WR2m * GR2) / R2 + T1

*2000 + T2 * 2000 ] / 32.2• Where R is the Drum or Wheel Radius D/2

• WR2m is the inertia of the motor rotor in ft2

• GR is the gear ratio of the motor to the drive• Note that the R2 terms are needed to convert rotating inertia to equivalent

mass

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Solving for the Deceleration Rate DR = ( B - W ) / M

• DR = Deceleration Rate

• M = Mass to be stopped

• W = Net unbalanced load (T1 - T2) * 2000

• B = Brake Rating in lbs linear force• Get B = BR / R

– BR is the Brake Rating in Ft*lbs

Applying the Deceleration Rate• Time to Stop = T = V / DR

• Braking Distance = S = (V/2) * T

Check Braking Distance Against Available or make sure you have the distance

Keope Hoist 91

The Gear Ratio Problem

GR = VM / VD• VM is rpm of motor at rated travel speed• VD is rpm of Drum

VD = V / (pi * D ) { remember I need rpm}

Solving for the Mass to be Stopped

Keope Hoist 92

Check Out Our Stopping Distance

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Yup – We Appear to Be OK