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 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 5 th gear to restrict velocity A better method would be to monitor tire temperature and pressure in real time

Real-time Measurement of Tire Temperature 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 T tire = T atm ) Dynamic calculation every 100 msec Tire load and speed determine temperature change Temperature drop by ambient heat loss: ΔT d = (T atm – T tire )·e -k d t where ΔT d = temperature decline (°C) T atm = ambient temperature (°C) T tire = current tire temperature(°C) k d = heat transfer coefficient (1.6 x ) t= time step (seconds)

Tire Temperature (continued) Temperature increase due to load and velocity: ΔT i = K T (1 – e -k i t ) – ΔT d whereΔT d = temperature increase (°C) K T = x (P + GMW)V k i = x (P + GMW)V 2 t= time step (seconds) ΔT d = 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

Tire wear rate reported by Miller Rubber Co. in 1928 Popular Mechanics, (1928). Burning 'em Up, June, 49(6), p (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 (Miller Rubber Co. graph, p.940) Wear rate as a function of tire temperature

Wear Rate = V 2 e -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) Wear rate as a function of tire temperature

Miller Tire Calculated wear rate = mm / 10, kph and 45 °C Calculated wear rate = mm / 10, kph and 45 °C Estimated Load (Miller tire) = 2.44 kg/cm 2 Load (CAT793) - full = 4.44 kg/cm 2 Load ratio = 1.82 Load (CAT793) - empty= 2.00 kg/cm 2 Load ratio = 0.82 Tire surface element contact ratio = 1.22 Road surface condition ratio = 12.5 CAT 793D Travelling fully-loaded= x 1.82 x 1.22 x 12.5 = 7.61 mm / 10,000 km Travelling empty= x 0.82 x 1.22 x 12.5 = 6.69 mm / 10,000 km Scale-up to a Haulage Truck tire

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 Validation from Real Tire Wear Data

Fuzzy Tire Wear Model (mm/10,000 km) Payload Velocity ZeroSlowModerateNormalFastVery Fast EmptyZeroLowestLowModerateNormalHigh SmallZeroLowestLowModerateNormalHigh QuarterZeroLowModerate NormalHigh HalfZeroLowModerateNormalHighVery-High Three-quartersZeroLowModerateNormalHighVery-High FullZeroModerateNormalHighVery-High Over FullZeroModerateNormalHighVery-HighMaximum 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 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 Velocity (kph) Acceleration Reaction Time Type Loaded Empty (m/s 2 ) (msec) Passive ± 100 Normal ± 100 Aggressive ± 50 Autonomous ± 0

Driver Behaviour – Aggressiveness Factor Aggressiveness Factor Stability Highly Stable Little Change Highly Variable Aggressiveness Passive-1.00 to to to Normal-0.10 to to to Aggressive+0.80 to to to +1.00

Driver Behaviour - 1 km modeled test drive