Mobile Equipment Power Requirements

L0CCE 4204

Mobile Equipment Power Requirements The constructor must select the proper equipment to relocate and/or process materials economically. The analysis procedure for matching the best possible machine to the project task requires inquiry into a machine to the project task requires inquiry into a machine’s mechanical capability. The engineer must first calculate the power required to propel the machine and its load. This power requirement is established by two factors:

1. Rolling Resistance2. Grade Resistance

Mobile Equipment Power Requirements Equipment manufacturers publish performance charts for individual machine models. These charts enable the equipment planner to analyze a machine’s ability to perform under a given set of job a machine’s ability to perform under a given set of job and load conditions.

Payload The payload capacity of construction excavation and hauling equipment can be expressed either volumetrically or gravimetrically. Volumetric capacity can be stated as struck or heaped Volumetric capacity can be stated as struck or heaped volume and either volume can be expressed in terms of loose cubic yard, bank cubic yard, or compacted cubic yard. The payload capacity of excavation buckets and hauling units is often stated by the manufacturer in terms of the volume of loose material, assuming that the material is heaped at a specified angle of repose

Machine PerformanceCycle time and payload determine a machine’s production rate, and machine travel speed directly affects cycle time.

The three power questions:1. Required Power2. Available Power3. Usable Power

Required Power Power required is the power needed to overcome resisting forces and cause machine motion. The forces resisting the movement of mobile The forces resisting the movement of mobile equipment are:1. Rolling Resistance2. Grade Resistance

Rolling ResistanceThe resistance of a level surface to constant-velocity motion across it.

Grade ResistanceThe force-opposing movement of a machine up a frictionless slope.

Total ResistanceTherefore, power required is the power necessary to overcome the total resistance to machine movement, which is the sum of rolling and grade resistance.

Total Resistance(TR) = Rolling Resistance(RR)+Grade Resistance(GR)

Mechanisms of Rolling Resistance

Rolling Resistance Varies with the Condition of the Surface

Rolling Resistance Varies with the Condition of the Surface

Rolling ResistanceThe maintenance of low-rolling resistance haul roads is one of the best financial investments an earthmoving contractor can make. The cost of having a grader to maintain the haul road is repaid in increased maintain the haul road is repaid in increased production.

Rolling Resistance The rolling resistance in pounds per gross ton is . . .

R = P (lbs.) W (tons)W (tons)

Where:R = Rolling resistance in pounds per tonP = Total tension in tow cable in poundsW = Gross weight of mobile vehicle in tons

Rolling ResistanceWhen tire penetration is known, an approximate rolling resistance value for a wheeled vehicle can be calculated . . .

RR = [40 + (30 * TP)] * GVWWhere:RR = Rolling resistance in poundsTP = Tire penetration in inchesGVW = Gross vehicle weight in tons

Grade AssistanceThe effect of gravitational force in aiding movement of a vehicle down a slope.

Grade Resistance/Assistance The force-opposing movement of a machine up a frictionless slope is known as grade resistance. It acts against the total weight of the machine, whether track type or wheel type.track type or wheel type. When a machine moves up an adverse slope, the power required to keep it moving increases approximately in proportion to the slope of the road. If a machine moves down a sloping road, the power required to keep it moving is reduced in proportion to the slope of the road. This is known as grade assistance.

Grade Resistance The most common method of expressing a slope is by gradient in percent. A 1% slope is one where the surface rises or drops 1 ft. vertically in a horizontal distance of 100 ft.vertically in a horizontal distance of 100 ft. If the slope is 5%, the surface rises or drops 5 ft. per 100 ft. of horizontal distance. If the surface rises, the slope is defined as plus, whereas if it drops, the slope is defined as minus.

Frictionless Slope-Force Relationships

Frictionless Slope-Force Relationships F = W sin α N = W cos α

For angles less than 10°, sin α ≈ tan α (the small –angle For angles less than 10°, sin α ≈ tan α (the small –angle assumption); with that substitution: F = W tan α tan α = V = G%

H 100

Frictionless Slope-Force Relationships F = W * G%

100If we substitute W = 2,000 lb/ton, the formula reduces If we substitute W = 2,000 lb/ton, the formula reduces to:

F = 20 lb/ton * G%This formula is valid for a G up to about 10%, that is, the small angle assumption (sin α ≈ tan α).

Total Resistance Total resistance equals rolling resistance plus grade resistance or rolling resistance minus grade assistance. It can also be expressed as an effective grade.

Rolling resistance expressed in lb/ton = G%20 lb/ton

Haul RoutesHauling efficiency is achieved by careful planning of haul routes.

Available Power Internal combustion engines power most construction equipment. Because diesel engines perform better under heavy-duty applications than gasoline engines, diesel duty applications than gasoline engines, diesel powered machines are the workhorses of the construction industry. Diesel engines have longer service lives and lower fuel consumption. Diesel fuel presents less of a fire hazard.

Work and Power Work is defined as force through distance.

Work = Force * Distance

Torque An internal combustion engine by the combustion of fuel in a piston develops a mechanical force that acts on a crankshaft having a radius r. The crankshaft in turn drives the flywheel and gears The crankshaft in turn drives the flywheel and gears that power the other components of the machine. The force from a rotating object, such as crankshafts (a “twisting” force), is termed torque.

The Relationship Between Horsepower and TorqueHorsepower (hp) = 6.2832 * rpm * Torque = rpm *Torque

33,000 5,25233,000 5,252 Conversely, to calculate torque . . .

Torque = 5,252 * hprpm

Horsepower Rating Manufacturers rate machine horsepower as either gross or flywheel (sometimes listed as net horsepower) Gross horsepower is the actual power generated by the engine prior to load losses for auxiliary systems, such engine prior to load losses for auxiliary systems, such as the alternator, air conditioner compressors, and water pump. Flywheel horsepower (fwhp) can be considered as usable horsepower. It is the power available to operate a machine-power the driveline-after deducting for power losses in the engine.

Rim pull Rim pull is a term that is used to designate the tractive force between the tires of machine’s driving wheels and the surface on which they travel. If the coefficient of traction is sufficiently high there If the coefficient of traction is sufficiently high there will be no tire slippage, in which case maximum rim pull is a function of the power of the engine and the gear ratios between the engine and the driving wheels. If the driving wheels slip on the supporting surface, the maximum effective rim pull will be equal to the total pressure the tires exert on the surface multiplied by the coefficient of traction.

Coefficient of TractionThe factor that determines the maximum possible tractive force between the powered running gear of a machine and the surface on which it travels.

Rim Pull EquationRim Pull = 375 * hp * efficiency (lb)

speed (mph)The efficiency of most tractors and trucks will range from 0.80 to 0.85 (use 0.85 if efficiency is not known).

Drawbar Pull The towing force a crawler tractor can exert on a load is referred to as drawbar pull. Drawbar pull is typically expressed in pounds. To determine the drawbar pull available for towing a To determine the drawbar pull available for towing a load it is necessary to subtract from the total pulling force available at the engine the force required to overcome the total resistance imposed by the haul conditions. If a crawler tractor tows a load up a slope, its drawbar pull will be reduced by 20 lb for each ton of weight of the tractor for each 1% slope.

Usable Power Usable power depends on project conditions: primarily, haul-road surface condition, altitude, and temperature.Usable force = Coefficient of traction * Weight onpowered running gear

Performance Charts Equipment manufacturers publish performance charts for individual machine models. These charts enable the equipment estimator/planner to analyze a machine’s ability to perform under a given to analyze a machine’s ability to perform under a given set of project-imposed load conditions. The performance chart is a graphical representation of the power and corresponding speed the engine and transmission can deliver. The load condition is stated as either rim pull or drawbar pull.

Rim Pull Performance Charts Required Power Total Resistance1. Estimate the rim pull (power) required – total resistance (rolling resistance plus grade resistance) –based on the probable job conditions.based on the probable job conditions.2. Locate the power requirement value on the left vertical scale and project a line horizontally to the right intersecting a gear curve.3. From the point at which the horizontal line intersects the gear curve, project a line vertically to the bottom x axes, which indicates the speed in mph.

Rim Pull Performance Charts Effective Grade Total Resistance1. Determine the machine weight both when the machine is empty and loaded. These two weights, empty and loaded, are often referred to as the net empty and loaded, are often referred to as the net vehicle weight and gross vehicle weight.2. Calculate a total resistance (the sum of rolling plus grade resistance both expressed as percent grade).3. Project a line horizontally from the intersection point of the vertical vehicle-weight projection and the appropriate total-resistance diagonal.

Rim Pull Performance Charts From the point at which the horizontal line intersects the gear range curve, project a line vertically to the bottom x axes, which indicates the machine speed in mph.machine speed in mph.

Retarder ChartA graphical presentation that identifies the controlled speed of a machine descending a slope when the magnitude of the grade assistance is greater than the rolling resistance.rolling resistance.