1
Steps in Design of a Hoisting System
©Dr. B. C. Paul 1999 major revision 2012
With Credit to Dr. H. Sevim for Original Book
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
2
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.
3
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
4
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
5
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!
6
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.
7
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
8
Input My Hoist Distance and
Production Rate Target
My Spreadsheet is
Opti-Hoist.
Next Lets look at some fixed
Cycle time elements
9
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

A fowl Beast
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.
11
Now We Need to Pick a Peak
Speed and a Rate of Skip
Acceleration
The maximum speed we lift at is safety related. For men there are regulations.
For materials there are guidelines (shown in pink)
12
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.
13
I’m going to go for modest speed
and particularly modest
acceleration
14
Geometry Considerations
Two Skips
Skip and Counter-weight
15
Stopping Considerations
Loading chute
If my controls miss
Stopping the skip at
The dump point – how
Far do I have for an
Emergency stop before
The over-wiend turns
Into a disaster?
Dump
Chute
Shaft Bottom
16
Getting Our First Estimate
Using a Nordberg approximation of the cycle time the program estimates the size
Of 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 or
A drum hoist).
17
Our Next Task is to Get Our
Exact Cycle Time
The only missing
Piece of information
Was what is the
Creep speed (2 ft/sec
Is reasonable).
(I want’s you money for my fake
Global warming initiative)
18
Next We Must Balance Skip Size,
Weight, Rope Diameters and
Wheel Sizes
19
First We Need to Pick A Skip Size
We have already been given a first guess skip size. We try about that size
And then check the actual hourly production achievable in the red box (we
Now have figured the exact cycle time too).
As can be seen a 16 ton skip will get me my 720 tons/hour.
20
Next I’ll Go for Skip Weight
In general a skip heavy enough to handle the banging of ore loading and
Unloading will weight about 75% of the load weight.
Opti-Hoist estimates this for us but leaves us a yellow blank to choose the
Weight. A higher weight usually means we are just adding weights to our
Skip.
21
Next We Go For Rope Sizing
Keope hoists usually have multiple ropes in even numbers, 2, 4, 6, and 8 being
Common. Where that 12 came from is unsure.
We need to consider both hoisting ropes and tail ropes. Sometimes tail ropes
Are used and worn-out hoist ropes which can cause tail ropes to be the same
As hoist ropes.
22
My First Guess is 4 ropes
(This is a relatively modest depth)
The red box estimates that I will need a 1.064 inch rope to reach needed
Safety factors for this depth.
23
From Here I Need to Go And
Enter My Rope Properties
I enter my rope size, it’s weight and it’s strength. (I have the advantage of
Having an estimate of what size rope to try).
The spreadsheet then compares the achieved factor of safety to what is required
24
Where Do I Get These Rope
Properties
The spreadsheet has a
Rope properties table
Right below for me to
Look things up on.
I’m looking for 1.064
Flattened strand
I go for 1.125
Weight 2.28 lbs/ft
Strength 57.9 tons
25
Enter My Rope and Check My
Factor of Safety
A 7 factor of safety clearly meets a 6.5
26
I Wonder If I Could Get Away
with a 1 inch rope
Eeee – one inch rope is a nope.
27
What if I Use High Strength
Steal?
Oh so close but still nope to the rope
28
With Hoist Rope Selected I can
now pick the Wheel for My Hoist
Frame
I need a 7.5 ft wheel (see pick recommendation) to avoid bending my rope to
Sharp. (You can see why I wanted a smaller rope – it would have allowed me
To use a smaller lower inertia wheel).
29
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.
30
I’m going to try straight across
Using my worn-out hoist ropes
for tail ropes.
31
Now I’ll Check Conditions at My
Keope Wheel
T1 is the weight of the heavy loaded side. T2 is the weight of the lighter empty
Side.
Remember – only friction stops the rope from slipping. The ratio of T1 to T2
Must therefor not be more than 1.5
Of course 1.95 is greater than 1.5 so life is sucking right now.
32
Another Parameter is Tread
Pressure
Keope wheels are normally lined with a leather like frictional material. Since we
Don’t want the ropes to cut the material to pieces we need to limit the load to
About 300 psi or less.
Well at least one thing worked.
33
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
34
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).
35
Putting 8 tons of Dead Weight on
My skips made it more even
Of course I’m still not there yet.
36
Ok – Adding 15.5 dead weight
tons to the skip did it!!!
Oh boy did it do it – take a look at that tread pressure.
37
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
38
There – A 10 ft Wheel Spreads
the Load
I know – the inertia situation sucks.
39
Come to Think About It – The
Factor of Safety Sucks Too
How profound – I put more weight on the rope without strengthening the rope
And I get into safety factor trouble.
(Where the
Money Goes)
40
Take A Little Weight Off the Skip
and Put A Little More On the
Rope
41
Time to Pick Out Our Motor
42
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
43
Hoist Duty Cycle
44
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
45
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
46
The Spreadsheet Does Your
Calculations
The Motor Sizing is
A function of something
Called EEW – what is
that.?
47
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.
48
Nordberg Equivalent Effective
Weight Chart
49
Reading the Chart
We know it is
A Keope hoist
So I will use
The Keope line.
I know I have
A 10ft wheel
So I start at
10 and read up
To the Keope
Line
50
I Then Read Over to the
Equivalent Effective Weight
I’ll be conservative
In my reading and
Call it 36,000 lbs
51
Enter the Number and Get Motor
Sizing
Of course understanding
What all these HP1, HPA
And TSL stuff is would
Add a lot of understanding
52
The Horsepower Demand of a
Keope Hoist Over Time Looks
Like This
Keope Hoist
53
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.
54
Keope Duty Cycles
Q - 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
55
a constant.
The Keope Duty Cycle
Q - 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.
56
Keope Duty Cycles
Q - 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.
57
Keope Cycles
Q - Why does the line slope down at the end of the Hoist
Cycle
A - The load is slowing down and accumulating less potential
58
energy per unit of time.
Keope Cycles
Q- Why the funny dashed lines that show more power
being used at the start and less being recovered at the end.
A - Frictional losses
59
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
Keope Hoist
60
You Can See Those Horsepowers
Calculated.
61
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
62
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
63
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
64
Horsepower #2 - Negative
Horsepower from Momentum
During Deceleration

HP2 = - TSL * V2 / (550 * g * Tr)
• Where Tr is time during deceleration
Keope Hoist
65
Horsepower #4 - Losses in Gears
and Drives


Derived empirically rather than by physics
fundamentals
HP4 = 0.111 * (2000 * SL * V / 550)
Keope Hoist
66
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
67
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
Keope Hoist
68
Yip – There are the values
69
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
Keope Hoist
70
Those Calculations are Done Too
71
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
Keope Hoist
72
And the Calculations Are There
73
RMS Equations Depend on
Motor Type

For AC Motor
 HPrms = [ ( HPD2 * Ta + HPB2* Tfs + HPE2* 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
Keope Hoist
74
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
75
Looks Like I Need About 1200
HP
76
Time to Pick the Motors
I need to choose the number and size of motor and the inertia of the rotor
77
Consider Picks
I’d rather go AC with frequency control. I’d like to do 2 600 hp motors but
With a 10 ft diameter Keope wheel I’ll still need gear reduction so I would
Only get about 94% transmission – My pick a 1250 two pole AC
78
Plug-In My Motor Parameters
and Gear Reduction Efficiency
Ok – That seems to work
(Note that there are limits to how much you can turn down the speed of
A motor with variable frequency drives)
79
Our Last Task is to Size the
Brake
80
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.
81
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
82
The Spreadsheet Runs the
Calculation
I need to set my brake rating to at least this size.
83
I Fill In the Numbers
Brake rating comes from the recommendation
Mass of the rotor came from the motor specification list
The gear ratio and speed were worked to get a workable
Ratio and a motor speed that was within the turn-down
Limit for the motor.
84
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.
85
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
86
Formula

Look at Maximum differential load
• W = (T1 - T2) * 2000
• T1 = Max load = SL + SW + (H * Wr * n/2000)
• T2 = Min Balancing Load = SW
87
The Spreadsheet Applies the
Formula to Get the Differential
Weight.
88
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
89
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
90
or make sure you have the distance
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}
Keope Hoist
91
Solving for the Mass to be
Stopped
Keope Hoist
92
Check Out Our Stopping
Distance
Yup – We Appear to Be OK
93