2. Checking for Traction Problems ©Dr. B. C. Paul 2000 revised 2008 Note – The methods outlined here are common practice in industry and can be found in a wide range of books. The slides specifically include tables from the Caterpillar Performance Handbook and the book Surface Mining from SME

3. The Traction Problem l Gradability and Retarder Charts give peak speed that engine can transfer power to wheels for l Does not guarantee the tire can transfer to ground without spinning l Max transfer of force F = coefric * Weight * cos(pheta)

4. The Traction Calculation l Coef of friction depends on road material primarily Generally get from table l Cos(pheta) term is usually almost 1 for 10% grade cos(pheta) = 0.995 Common practice to take as unity l Weight is weight on Drive Wheels (in lbs) - important distinction for two wheel drives

5. Getting Coef of Friction from Table Crushed Rock or Gravel Would Be Common in a Quarry

6. Also Need Distribution of Weight from Specs

7. Example l Cat on the Hill Empty weight is 87000 lbs Distribution empty is 53% to rear wheels or 46,000 lbs Loaded weight is 204,000 lbs Distribution Full is 67% to rear wheels or 137,000 lbs Note that this truck was weight limited and reached gross weight limit - volume limited truck would not.

8. Example Cont. l It’s a Quarry so road is gravely - sometimes rains so worse case may be wet gravel From Table 0.35 is coef of friction l Could have considered icy conditions after freezing rain But would you run that way? Quarries often close in winter because of slabbing from face

9. Plugging into the Tire Spin Equation l 137,000 lbs * 0.35 * 0.995 = 48,000 lbs loaded l 46,000 lbs * 0.35 * 0.995 = 16,000 lbs empty l Like Wow Man - Awsome Numbers. Now What do I do with them?

10. Determining if Tire Spinning is Occurring l Answer comes in lbs force that can be transferred between the tire and the ground l This has the form of Rimpull l Compare the number to the Rimpull required to propel the truck (or keep it from sliding down hill out of control)

11. Getting the Rimpull l Rimpull to hold back empty truck 43.5 tons * 115 lbs/ton = 5,000 lbs l Wait! Hold Everything - That’s downhill so 115 lbs/ton must be negative The tire doesn’t know who’s pulling who - only whether the friction is enough to balance the force

12. Making the Comparison l For Empty Truck Going Downhill Rimpull Required is 5,000 lbs Traction Force Available is 16,000 lbs 5,000 < 16,000 so I’m OK l For Loaded Truck Rimpull Required is 29,000 lbs 29,000 < 48,000 lbs

13. Gee This is So Much Fun I Can’t Wait to Do it for Every Segment on My Haul Road l Actually - You Don’t Have to l We are comparing two numbers Rimpull Needed = lbs/ton * Total Tons Weight Traction Available = coefric * Drive Wheel Weight l In Simple Terms RN = K 1 * Tweight TA = K 2 * Dweight

14. The Discovery l Both Equations are a Linear Function of Weight On a ton for ton basis the rimpull needed is the same loaded or unloaded Traction depends on portion of that weight on drive wheels The Traction Value is minimum when the truck is empty

15. Checking in Critical Spots l If the Empty Truck won’t spin - the loaded Truck won’t l Look for points of maximum total grade - gives maximum rimpull l Look for points of low coef of friction - minimizes Traction l Check Those Points

16. Application to Our Example l Our haul road is uniform so we have no minimal coef of friction l Our haul road is uniform so we have no higher rolling resistance l Thus maximum grade will be the worst case coming out where the two resistances are additive

17. The Critical Check Point l Loaded Truck Coming Out and Empty Truck Going in - We’ve already checked l There is a non routine point - what if we have to take a truck out empty? In checking truck and road compatibility usually check things that are realistic

18. Check to See if We Can Get Out Empty l 43.5 tons * 285 lbs/ton = 12,400 lbs l Compare Rimpull Needed 12,400 lbs Traction Available 16,000 lbs l I’m Still Ok

19. How Does FPC Do It? l You have entered haulage profile and frictional forces l You have picked trucks and all tables including weight distributions are loaded l FPC checks all segments for spinning If a problem occurs it gives an error message l FPC only checks regular haul segments What if you need to bring an empty truck out of the pit when a loader break-down occurs?