Engine Design Process Load Factor
Displacement
Bore/Stroke Ratio

Load Factor :

Load Factor Load factor is the ratio of average power output to maximum power output.
Gasoline engines typically are designed with a load factor of 0.3 while diesel engines are designed with load factors close to 1.0.

Selection of Displacement :

Selection of Displacement After rated speed and power is specified, the next step is to select the displacement.
Typical pbme pressures range from 700 to 900 kPa are reasonable.

Bore/Stroke Ratios :

Bore/Stroke Ratios Typical bore/stroke ratios range from 0.84 to 0.96.
Extreme values range from 0.79 to 1.30.
Lower bore/stroke ratios facilitate higher compression ratios – more air flow supports higher power output.

Engine Timing and Firing Order :

Engine Timing and Firing Order Engine cylinders are numbered from front to back on in-line engines.
For “V” engines, the cylinders are numbered front to back on the left then right banks.
Alternate numbering scheme for “V” engines is the order (front to back) in which pistons are connected to the crank.

Direction of Rotation :

Direction of Rotation Standard direction of crankshaft rotation is clockwise when the crank is viewed from the front of the engine.

Fig. 6.1: Two-Cylinder Firing Order :

Fig. 6.1: Two-Cylinder Firing Order Special slide for Brandon!!!!

Piston Crank Dynamics The piston position as a function of crank angle,
where S is the piston position from HDC, R is the crank throw, and L is the connecting rod length.

Fig. 6.4: Crankshaft with Counterweights :

Fig. 6.4: Crankshaft with Counterweights

Piston Crank Dynamics :

Piston Crank Dynamics The previous equation can be simplified to,
using a binomial series expansion.

Piston Crank Dynamics :

Piston Crank Dynamics Differentiating the previous equation, velocity becomes,
where

Piston Crank Dynamics :

Piston Crank Dynamics Differentiating the previous equation, acceleration becomes,
where a is acceleration.

Piston Inertial Force :

Piston Inertial Force Using Newton’s Law and the previous equation,
where m is piston/connecting rod mass, and F is the force generated when accelerating this mass.

Fig. 6.5: Piston-Crankshaft Dynamics :

Fig. 6.5: Piston-Crankshaft Dynamics

Effective Mass of Connecting Rod :

Effective Mass of Connecting Rod The portion of the connecting rod mass added to the piston mass is,
where b and L are specified in Fig. 6.5.

Reciprocating Unbalance in Single-Cylinder Engines :

Reciprocating Unbalance in Single-Cylinder Engines The oscillating force in the x-direction (vertical) becomes,
where mp is the mass of the piston, mc1 and mc2 are masses of the connecting rod, and me is the mass of the crank pin.

Effective Mass of Crankpin :

Effective Mass of Crankpin The effective mass of the crankpin is determined as,
where mcp is the mass of the crankpin, mca is the mass of the material supporting the crankpin, mcb is the mass of the counterweight opposite the crankpin, R is the crankpin radius (1/2 the stroke), and Ra and Rb are the radii to the respective crankshaft masses.

Reciprocating Unbalance in Single-Cylinder Engines :

Reciprocating Unbalance in Single-Cylinder Engines The oscillating force in the y-direction (horizontal) becomes,

Primary and Secondary Shaking Forces :

Primary and Secondary Shaking Forces The oscillating forces (both x and y directions) have components at two frequencies.
The primary shaking force occurs at engine speed.
The secondary shaking force occurs at twice the frequency of engine speed.
Counterweights are sized to cancel half of the vertical primary shaking force, larger masses would increase the lateral primary shaking force to an unacceptable level.

Reciprocating Unbalance in Multi-Cylinder Engines :

Reciprocating Unbalance in Multi-Cylinder Engines The Fx forces are added together for multi-cylinder engines – proper phase angle must be included.
“Lanchester Balancers” are often used in 4-cylinder engines to cancle the secondary shaking force (used as the tractor frame) to protect the operator from vibration

Table 6.1: Amplitude of Shaking Forces :

Table 6.1: Amplitude of Shaking Forces

Fig. 6.6: Lanchester Balancer :

Fig. 6.6: Lanchester Balancer

Inertial Couples :

Inertial Couples Inertial couples (Table 6.1) tend to make the engine rock about the y-axis (coinciding with the centerline of the crankshaft).
Three-cylinder engines have provisions for balancing half of the primary couple by use of a counterweighted front pulley.
Unfortunately, the counterweighted pulley generates a new yawing couple about the z-axis.

Instantaneous Torque and Flywheels :

Instantaneous Torque and Flywheels Instantaneous torque is a product of Qt and R. The end result is summarized as,

Fig. 6.5: Piston-Crankshaft Dynamics :

Fig. 6.5: Piston-Crankshaft Dynamics

Fig. 6.7: Instantaneous Torque :

Fig. 6.7: Instantaneous Torque

Radial Force at Crankshaft :

Radial Force at Crankshaft If the forces at the top of the piston is known (Fp), then the radial force (Qr) at the crankshaft becomes,

Flywheel Design :

Flywheel Design Instantaneous torque is less than average torque (Tave) for most of the cycle.

Flywheel Design :

Flywheel Design Average output torque is equal to the load torque on the engine.
When the average torque drops below load torque, the engine stalls!
When the instantaneous torque is greater than load torque, the flywheel accelerates and stores energy.
When the instantaneous torque is less than load torque, the flywheel gives up kinetic energy.

Fig. 6.8: Instantaneous Toque for 4 and 6 Cylinder Engines :

Fig. 6.8: Instantaneous Toque for 4 and 6 Cylinder Engines

Required Mass Moment of Inertia :

Required Mass Moment of Inertia Mass moment of inertia can be estimated as,
where DE is the kinetic energy transfer and k is the speed variation coefficient.

Required Mass Moment of Inertia :

Required Mass Moment of Inertia The kinetic energy transfer can be estimated as,
where W is the indicated work per revolution and l is a ratio from Table 6.2.

Table 6.2: Approximate Flywheel Constants :

Table 6.2: Approximate Flywheel Constants

Required Mass Moment of Inertia :

Required Mass Moment of Inertia The speed variation is obtained from the following relationship,
where p is the percent of allowable speed variation.

Required Mass Moment of Inertia :

Required Mass Moment of Inertia Please recall the indicated work can be estimated as,

Vibration Dampeners :

Vibration Dampeners Instantaneous torques tend to twist the crankshaft.
Higher harmonics from these torque fluctuations can approach the natural frequency of the crankshaft.
More problematic with long crankshafts (in-line 6 cylinder engines).
Problem is corrected by mounting a small flywheel to the front of the crankshaft – connection is flexible.

Fig. 6.9: Vibration Dampeners :

Fig. 6.9: Vibration Dampeners

Homework Set No. 5 :

Homework Set No. 5 Do the even problems at the end of Chapter 6 for next Tuesday.

Footnote: 2001 smart fortwo cdi :

Footnote: 2001 smart fortwo cdi In view of the limited space available, installing a hybrid drive unit into the smart fortwo cdi, was an enticing prospect for the DaimlerChrysler engineers. This smallest prototype from DaimlerChrysler hybrid vehicles is fitted with a 20 kW/28 hp electric motor, which together with the three-cylinder diesel engine constitutes a space-saving unit developing 30 kW/41 hp. The drive unit is a winner on all three counts: reduced fuel consumption, enhanced ride comfort and favorable acceleration with practically no interruption to tractive force.

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