Modeling Tire Wear and
Driver Behaviour in
Open Pit Haulage Operations
ExtendSIM Software
• Dynamic modeling of real-world processes
• Uses building blocks to explore processing steps
• Benefits
• Easy to use
• Inexpensive
• MS-Windows environment
• Handles both Discrete and Deterministic Models
Discrete and Deterministic
• Discrete Events
• Probabilistic method
• Maintenance, Loading, Dumping
• Deterministic
• First Principles
• Truck movement
– Fuel consumption
– Tire temperature
• Fuzzy Models (A.I.)
• Road conditions (rolling resistance and traction)
• Tire wear
• Driver behaviour (velocity, acceleration, reaction time)
Fuzzy Road Conditions
• Rolling Resistance varies from
2.5% to 3.5%
• Traction varies from
0.44 to 0.55
• Value depends on schedule for
grader and water truck and
rain/snow intensity/duration
Rolling Resistance Fuzzy Model
Conventional Approach to Tire Wear
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All tire suppliers use the TKPS (TMPS) method
Tonnes-Kilometers per Hour
Actually, this is simply an Alarm System
If TKPH is exceeded on a real-time basis, the
truck is prevented from operating in 5th gear
to restrict velocity
• A better method would be to monitor tire
temperature and pressure in real time
Real-time Measurement of Tire Temperature
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External chassis-mounted IR temperature sensor
Temperature sensor embedded in tire tread
External sensor subject to ambient conditions (shade/sun)
Embedded sensor can wirelessly
send data to on-board computer
Tire Temperature Decline (until Ttire = Tatm)
• Dynamic calculation every 100 msec
• Tire load and speed determine temperature change
• Temperature drop by ambient heat loss:
ΔTd = (Tatm – Ttire)·e-kd t
where ΔTd = temperature decline (°C)
Tatm
Ttire
kd
t
= ambient temperature (°C)
= current tire temperature(°C)
= heat transfer coefficient (1.6 x 10-4)
= time step (seconds)
Tire Temperature (continued)
• Temperature increase due to load and velocity:
ΔTi = KT(1 – e-kit) – ΔTd
where
ΔTd = temperature increase (°C)
KT
= 8.344 x 10-3(P + GMW)V
ki
= 6.836 x 10-7(P + GMW)V2
t
= time step (seconds)
ΔTd = temperature decline (°C)
P
= payload (tonnes)
GMW = gross machine weight + fuel (tonnes)
Tire Temperature Change
Tire temperature cycles (14.7% idle time)
Velocities = 16 kph loaded / 32 kph empty
Tire temperature cycles (9.3% idle time)
Velocities = 16 kph loaded / 32 kph empty
Tire temperature cycles (9.3% idle time)
Velocities = 19 kph loaded / 38 kph empty
Wear rate as a function of tire temperature
Tire wear rate reported by Miller Rubber Co. in 1928
Popular Mechanics, (1928). Burning 'em Up, June, 49(6), p.938-942. (Miller Rubber Co. graph, p.940)
Wear rate as a function of tire temperature
Tire wear rate reported by Miller Rubber Co. in 1928
Popular Mechanics, (1928). Burning 'em Up, June, 49(6), p.938-942. (Miller Rubber Co. graph, p.940)
Wear rate as a function of tire temperature
Wear Rate = 21.699V2e-7,106/RT + 11,931Ve-8,621/RT
There are two terms in the equation:
First term relates to Energy flow through the tire
Second term relates to force (momentum of tire)
Scale-up to a Haulage Truck tire
Miller Tire
Calculated wear rate = 0.274 mm / 10,000 km @ 15 kph and 45 °C
Calculated wear rate = 0.528 mm / 10,000 km @ 25 kph and 45 °C
Estimated Load (Miller tire) = 2.44 kg/cm2
Load (CAT793) - full
= 4.44 kg/cm2
Load (CAT793) - empty = 2.00 kg/cm2
Load ratio = 1.82
Load ratio = 0.82
Tire surface element contact ratio = 1.22
Road surface condition ratio = 12.5
CAT 793D
Travelling fully-loaded = 0.274 x 1.82 x 1.22 x 12.5 = 7.61 mm / 10,000 km
Travelling empty
= 0.528 x 0.82 x 1.22 x 12.5 = 6.69 mm / 10,000 km
Validation from Real Tire Wear Data
CAT 793D
Travelling fully-loaded = 7.61 mm / 10,000 km
Travelling empty
= 6.69 mm / 10,000 km
Average
= 7.15 mm / 10,000 km
Calculated Tread Depth Change = 7.15 x 11 = 78.7 mm
Mine Data
Typical Tread Depth Change at scrap = 75 mm for ~ 110,000 km (5,500 hrs)
Error = 4.9%
Assumed Maximum Wear Rate = 10 mm / 10,000 km
Fuzzy Tire Wear Model (mm/10,000 km)
Payload
Velocity
Moderate
Normal
Low
Moderate
Empty
Zero
Zero
Slow
Lowest
Fast
Normal
Very Fast
High
Small
Zero
Lowest
Low
Moderate
Normal
High
Quarter
Zero
Low
Moderate
Moderate
Normal
High
Half
Zero
Low
Moderate
Normal
High
Very-High
Three-quarters
Zero
Low
Moderate
Normal
High
Very-High
Full
Zero Moderate
Normal
High
Very-High
Very-High
Over Full
Zero Moderate
Normal
High
Very-High
Maximum
Three main factors: payload, speed, tire temperature
Additional factors: tire pressure, road conditions, tire rotation
Tire Wear Model based on Fuzzy Logic
Calibration factors: maximum tire wear rate = 10 mm / 10,000 km
maximum velocity = 35 kph
maximum payload = 440 tonnes (average = 219 tonnes)
Driver Behaviour Sub-Model
Behaviour Criteria
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Driving Speed
Acceleration
Braking
Reaction Time
Lateral Position Control
• Many factors –gender, energy level, age, health, family
and personal issues, tiredness, skill level,
time since training, personality, time in
shift, time in work period
• Too many variables and far too complex to validate
Driver Behaviour – Aggressiveness Factor
Driver Behaviour – Set Points (average)
Driver
Type
Passive
Normal
Aggressive
Autonomous
Velocity (kph)
Acceleration Reaction Time
Loaded Empty
(m/s2)
(msec)
12
22
0.31
400 ± 100
15
26
0.42
300 ± 100
18
30
0.70
250 ± 50
13
23
0.42
100 ± 0
Driver Behaviour – Aggressiveness Factor
Stability
Aggressiveness Factor
Aggressiveness
Highly Stable
Little Change
Highly Variable
Passive
-1.00 to -0.80
-1.00 to -0.50
-1.00 to -0.20
Normal
-0.10 to +0.10
-0.25 to +0.25
-0.40 to +0.40
Aggressive
+0.80 to +1.00
+0.50 to +1.00
+0.20 to +1.00
Driver Behaviour - 1 km modeled test drive