Modelling Truck Performance in a Spread-sheet

Introduction

Most open pits today are mined using the truck and shovel mining system (refer Figure 1).

These operations usually model their mining schedules and cost models using a spread-sheet.

However, truck performance and ultimately haulage requirements (that is truck numbers) are usually modelled in a specialised truck haulage program such as TALPACTM.

As discussed here, truck performance and haulage requirements can be modelled in a spread-sheet, there are some simple formulas which can be applied with significant benefits.

Figure 1 Truck and shovel in operation

Description: Truck and shovel in operation

Modelling truck performance in a spread-sheet

The physics or mathematics behind the truck performance is not difficult and the results match well with truck manufacturer’s performance graphs.

The calculation of fuel burns is also presented here.

Fuels burns are of interest because of the impact of increasing fuel prices and because they are often based on historical usage rather than calculated as part of the truck performance.

The physics of a truck

The up ramp truck speed is dependent on the energy available from the engine to lift the truck weight, including its payload, against gravity and to overcome rolling resistance and transmission losses (refer Figure 2 and Equation 1).

Figure 2 Rolling resistance model (images courtesy www.hitachimining.com)

Description: Rolling resistance model


Equation 1: Up ramp truck speed

  UpRampTruckSpeed=3.6*GrossEnginePower*TransmissionEfficiency*(1+RampGrade*RampGrade)^0.5
                   TotalTruckWeight*9.81*(RampGrade+RollingResistance)

 

The down ramp truck speed is dependent on the energy that engine can absorb generated by the truck running downhill from gravity but less rolling resistance and transmission losses (refer Equation 2).

Equation 2: Down ramp truck speed

  DownRampTruckSpeed=-3.6*GrossEnginePower*RetarderFactor*1+RampGrade*RampGrade)^0.5
                     TotalTruckWeight*9.81*(RampGrade+RollingResistance)

In both cases the maximum truck speed needs to be limited to the manufacturer’s recommendation.

Further speed restrictions may be applied for site specific (i.e. safety) reasons.

The gross engine power (in kilowatts), trucks weights [maximum and unloaded (in tonnes)] are published in the truck manufactures manuals.

The transmission efficiency factor and the retarder factor are used to calibrate the model to the manufacturer’s performance graph.

An 80% transmission efficiency and a 115% retarder factor seems to work universally.

Figure 3 shows the model plotted against the Caterpillar 777D truck (using the performance graph and assuming 3% rolling resistance, refer Figure 4).

The up ramp performance calibration is very good. The down ramp performance approximates the “gear” speeds. This is considered sufficient for most applications.

Figure 3 Truck model calibration

Description:Truck model calibration


Figure 4 Caterpillar 777D truck performance graphs (images courtesy Caterpillar handbook)

Description: Caterpillar 777D truck performance


Electric trucks and trolley assist

The model will work for electric trucks and trolley assist applications but calibration of the transmission efficiency and retarder factors may be required.

Retarder options

Some trucks have additional retarder capacity options. In these cases the retarder factor would have to be increased.

Engine load

The engine loading (up ramp) is calculated in Equation 3.

Equation 3: Engine loading

  EngineLoading=UpRampTruckSpeed*TotalTruckWeight*9.81*(RampGrade+RollingResistance)
                3.6*GrossEnginePower*TransmissionEfficiency*(1+RampGrade*RampGrade)^0.5

Fuel consumption

Fuel burn estimates are approximate (+/-10%) (refer Equation 4).

Equation 4: Fuel burns

  FuelBurn=23.3%*GrossEnginePower*(EngineLoading*96%+4%)

The 23.3% factor seems to be a reasonable average estimate.

If the maximum fuel burn is known for the truck type then the factor can be re-calculated (refer Equation 5).

Equation 5: Fuel burn factor

  FuelBurnFactor=MaximumFuelBurn
                 GrossEnginePower

Practical application

Table 1 contains the formulas previously discussed in a simple model for the Hitachi EH4500 truck.

The key assumption is that the haulage profile segments can be re-calculated into an equivalent profile using level, up 10% or 10% down, segments.

Real haulage profiles never meet this constraint but the error resulting from the assumption is not considered significant.

Table 1 The EH4500 truck performance model

EH4500LevelUp RampDown Ramp
Truck parameters:   
Grade0.0%10.0%-10.0%
Engine power (kw)2,0142,0142,014
Transmission efficiency80%80%80%
Retarder Efficiency115%115%115%
Rolling resistance2.5%2.5%2.5%
Loaded Performance:   
Loaded weight479479479
Loaded Speed Limit45.030.030.0
Speed45.09.923.8
Engine Power91%100%0%
Fuel Consumption (ltr/hr)42946914
Unloaded Performance:   
Unloaded weight211211211
Unloaded Speed Limit45.030.030.0
Speed45.022.530.0
Engine Power40%100%0%
Fuel Consumption (ltr/hr)19746914


Notes:


The unloaded weight is from the manufacturer’s handbook but could be increased if necessary to allow for “carry-back” (that is material stuck to the truck tray).

Table 2 illustrates the extraction of the key data for truck modelling.

Table 2 Rationalised EH4500 truck performance

Truck Speeds (km/hr)LoadedUnloaded
Level4545
Up Ramp9.922
Down Ramp2430
Truck Fuel Burns (l/hr)LoadedUnloaded
Level429197
Up Ramp469469
Down Ramp1414
Idle1414

Table 3 Schedule truck capacity, effective operating time and cycle delays

Truck Schedule DataValues
Unloaded Truck Weight198
Maximum Truck Weight480
Carry Back5%
Nominal Capacity100%
Moisture (%)4%
Productive Hours per Year6600
Effective Minutes per Hour50
Queue & Spot 1.0
Load2.5
Dump1.0

Table 4 presents an example haulage profile.

Table 4 Haul profile

Haul DistancesValues
Forward Trip (Loaded): 
Queue & Spot  
Load 
Level800
Up Ramp1,800
Down Ramp300
Return Trip (Unloaded): 
Dump 
Up Ramp300
Down Ramp1,800
Level800
Total Metres5,800

Using the truck speeds from Table 2 and haul distances from Table 4, the cycle time can be calculated (refer Table 5).

Table 5 Cycle times

Cycle TimeValues
Forward Trip (Loaded): 
Queue & Spot 1.00
Load2.50
Level1.07
Up Ramp10.89
Down Ramp0.76
Return Trip (Unloaded): 
Dump1.00
Up Ramp0.80
Down Ramp3.60
Level1.07
Cycle Time21.68

Using the truck fuel burns from Table 2 and cycle time components from Table 5 the fuel burns can be calculated (refer Table 6).

The fuel burn per effective hour (50 minute hour) is the fuel burn per cycle multiplied by the cycle time.

Table 6 Fuel burns

Fuel BurnValues
Forward Trip (Loaded): 
Queue & Spot 0.23
Load0.59
Level7.63
Up Ramp85.15
Down Ramp0.18
Return Trip (Unloaded): 
Dump7.82
Up Ramp6.26
Down Ramp0.84
Level3.51
Litres/Cycle104.39
Litres/Effective Hour288.92

Table 7 presents the final truck productivity and fuel burn per productive hour.

Table 7 Final Truck productivity and fuel burns

Truck Cycle Time and Fuel Burn CalculationsValues
Truck productivity (tonnes) per Productive Hour593
Truck Fuel Burn (kilolitres) per Productive Hour243
Truck productivity (tonnes) per Year3,912,381

Sensitivities

For the practical example above, a 2.5% rolling resistance was applied. This value is suitable for good road conditions.

What would happen if the rolling resistance was 3% and the maximum level speed reduced to 30km/hr (from 45km/hr)?

The model (refer Table 8) suggests that productivity would fall about 6% (or haulage costs would rise about 6%).

Table 8 Truck productivity for 3% rolling resistance and a 30km/hr speed limit

Truck Cycle Time and Fuel Burn CalculationsValues
Truck productivity (tonnes) per Productive Hour555
Truck Fuel Burn (kilolitres) per Productive Hour241
Truck productivity (tonnes) per Year3,661,768

Conclusion

The modelling of truck performance directly in a spread-sheet is not particularly difficult and allows tighter integration of the schedule and cost model.

Useful for “what if” scenarios, as demonstrated above.

If you would like a copy of the spread-sheet used above, click the link (TruckModelling.xlsx).


You can contact me at Master@AlanCooper.id.au if you feel the need.



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