Modeling Tire Wear and Driver Behaviour in Open Pit Haulage Operations

1. Modeling Tire Wear and Driver Behaviour in Open Pit Haulage Operations

2. 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

3. 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)

4. 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

5. Rolling Resistance Fuzzy Model

6. 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 5th gear to restrict velocity • A better method would be to monitor tire temperature and pressure in real time

7. 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

8. 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-kdt where ΔTd = temperature decline (°C) Tatm = ambient temperature (°C) Ttire= current tire temperature(°C) kd = heat transfer coefficient (1.6 x 10-4) t = time step (seconds)

9. 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)

10. Tire Temperature Change

11. Tire temperature cycles (14.7% idle time) Velocities = 16 kph loaded / 32 kph empty

12. Tire temperature cycles (9.3% idle time) Velocities = 16 kph loaded / 32 kph empty

13. Tire temperature cycles (9.3% idle time) Velocities = 19 kph loaded / 38 kph empty

14. 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)

15. 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)

16. 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)

17. 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 ratio = 1.82 Load (CAT793) - empty = 2.00 kg/cm2 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

18. 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

19. Fuzzy Tire Wear Model (mm/10,000 km) Three main factors: payload, speed, tire temperature Additional factors: tire pressure, road conditions, tire rotation

20. 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)

21. Driver Behaviour Sub-Model

22. 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

23. Driver Behaviour – Aggressiveness Factor

24. Driver Behaviour – Set Points (average) Driver Velocity (kph) Acceleration Reaction Time Type Loaded Empty (m/s2) (msec) Passive 12 22 0.31 400 ± 100 Normal 15 26 0.42 300 ± 100 Aggressive 18 30 0.70 250 ± 50 Autonomous 13 23 0.42 100 ± 0

25. Driver Behaviour – Aggressiveness Factor

26. Driver Behaviour - 1 km modeled test drive