# Reciprocating engine

Fig. 1: Schematic drawing of a reciprocating piston engine

In a reciprocating piston engine , the expansion of a gas via a slider crank causes mechanical energy to be released or work to be performed. Reciprocating piston engines are piston machines .

## Working principle

The expansion of the gas in a cylinder does work on a piston , which is transferred to the crankshaft through a connecting rod . The oscillating movement of the piston is converted into a rotary movement , and the pistons can deliver work to the crankshaft via the connecting rods (Fig. 1). Two designs are known:

• In the case of the stationary engine, the engine housing is fixed with the cylinders and the crankshaft rotates. This design is the norm today.
• In a rotary engine , the motor housing rotates around the crankshaft. It can stand still or also rotate, being coupled to the engine housing via gears, for example on the Megola motorcycle. The cylinders revolve around the crankshaft axis. The crank pins are arranged eccentrically, which creates the stroke of the individual pistons in the cylinders, just like with the stationary engine. Early aircraft engines were often star- rotating engines.

If you only consider the movement of the parts relative to one another, the two designs do not differ. The cylinders of a radial engine are arranged rotationally symmetrically around the crankshaft, which prevents imbalance. Their number is usually odd in four-stroke engines , so that the ignitions take place at regular intervals.

Examples of reciprocating engines are:

Reciprocating engines are also classified according to the number and arrangement of pistons per combustion chamber:

• normal reciprocating engine with one piston per combustion chamber (by far the most common)
• Double piston engine with two pistons in parallel cylinders, with a common combustion chamber and coupled lifting movement
• Opposite piston engine with two pistons working against one another and coupled stroke movement in the same cylinder

They are also classified according to the number and arrangement of the cylinders:

## Terms and designations

• The crank drive or the engine (colloquially) converts the force of the gas expansion into an oscillating movement of the piston and then into a rotating movement of the crankshaft and controls the gas exchange process, as well as other synchronous processes, if necessary. Further components of the crankshaft drive are piston rings, piston pins , connecting rods and crankshafts.
• The piston slides up and down in the cylinder . The piston rings seal the expansion space between the piston and cylinder so that the gas charge cannot expand past the piston.
• The piston forms a movable wall in the expansion space. The movement converts the expansion of the gas into mechanical work. In addition, the piston may, in some designs (especially two-stroke engines ), gas exchange (with internal combustion as gas exchange hereinafter) control.
• The piston reverses its movement at the dead center . The top dead center (TDC) is reached when the expansion chamber has the smallest volume, which in internal combustion engines as a compression volume (V C is referred to). The bottom dead center (BDC) is reached when the expansion space reaches its largest volume.
• The displacement (V H ) is the difference between the cylinder volume in BDC and TDC.
• In the internal combustion engine, the ratio of compression volume and maximum combustion chamber volume, i.e. ε = 1+ V H / V C, is referred to as the geometric compression ratio (ε). It is usually given as 1: ε.
• The design describes the arrangement of the cylinders in engines with more than one cylinder. Frequently used designs are in- line engines , V-engines , boxer engines and occasionally the W-engine . Star , double piston and opposed piston engines can only be found in model making today.
• Mass forces are created by the movement of the crank mechanism on each cylinder. The cause is the oscillating movement of the piston, the rotating movement of the crankshaft and the complex superposition of both parts in the movement of the connecting rod.
• The vibrations of the engine can be reduced by balancing out inertia forces. A simple compensation can be achieved by using balance shafts . Balance shafts rotate at the crankshaft speed or twice the crankshaft speed (example Lanchester compensation ). In addition, more complex systems such as compensating connecting rods ( e.g. BMW F800 ) are used.
• Mass moments arise around the center of gravity of the engine through the interaction of several cylinders through the movement of the individual pistons, for example when one piston goes up and the other goes down at the same time. A suitable number and arrangement of the cylinders can eliminate moments of inertia.
• The crank angle is measured between the cylinder longitudinal axis and the crank pin of the crankshaft and counted in the direction of the crankshaft rotation. In Otto engines, the ignition point (ignition angle) is related to the crank angle, negative angles are often specified as "φ degrees before TDC". In the case of the four-stroke engine, counting is occasionally continued over all working cycles, so that the crank angle can be between 0 and 720 °.
• Torsional vibrations arise from the periodic excitation of the gas forces and generate an uneven output torque on the crankshaft and possibly a clutch.
• The ignition sequence of an internal combustion engine (also referred to as this for diesel engines) indicates the sequence of combustion in multi-cylinder engines. As a rule, care is taken to ensure that the ignitions take place at the same intervals in relation to the angle of rotation of the crankshaft in order to reduce torsional vibrations.
• The flywheel also serves to limit the torsional vibrations and as an intermediate store for the energy, particularly in the case of the internal combustion engine, in which energy has to be provided for the compression of a cylinder during the compression phase.
• The gas exchange is controlled by valves (four-stroke and some two-stroke large engines), rotary slide valves (two-stroke, rarely four-stroke), lamellar or sniffer valves (two-stroke) or slots (especially two-stroke and Wankel engines).

## Mass forces

As a result of the stroke movement of the pistons and connecting rods, as well as the non-uniform transmission behavior of the crank drive , inertial forces occur which are supported in the engine bearings and cause neighboring structures to vibrate .

The inertia forces of the linearly moving parts of the crank mechanism (oscillating masses) can be approximately calculated using the following formula:

${\ displaystyle F _ {\ mathrm {osz}} = m _ {\ mathrm {osz}} \ cdot r \ cdot \ omega ^ {2} \ cdot (\ cos (\ alpha) + \ lambda \ cdot \ cos (2 \ , \ alpha))}$

With

${\ displaystyle \ lambda = {\ tfrac {r} {l}}}$
${\ displaystyle F _ {\ mathrm {osz}}}$: Oscillating inertial force
${\ displaystyle m _ {\ mathrm {osz}}}$: Oscillating mass
${\ displaystyle r}$: Crank radius
${\ displaystyle \ omega}$: Angular speed of the crankshaft
${\ displaystyle \ alpha}$: Crank angle
${\ displaystyle l}$: Connecting rod length
${\ displaystyle t}$: Time since the top dead center was passed

Since the expression in brackets is about the first two members of a series expansion, it is referred to as 1st order inertial force and 2nd order inertial force. ${\ displaystyle \ cos (\ alpha)}$${\ displaystyle \ lambda \ cdot \ cos (2 \, \ alpha)}$

Theoretically, there are not only 1st and 2nd orders, but an infinite number of integer orders, which, however, are mostly negligible from the 4th order due to their small size.

## Mass balancing

Fig. 2: Lanchester compensation

The rotating masses of the crankshaft drive can be balanced by counterweights on the crankshaft. Oscillating inertia forces of the 1st and 2nd order can be avoided or reduced in multi-cylinder engines by a clever arrangement of the cylinders. In order to fully compensate for these inertia forces, at least six cylinders are required for a four-stroke in- line engine or eight cylinders for a V-engine . In engines with fewer cylinders, balancer shafts are often used, on which the corresponding balancing imbalances rotate with single or double crankshaft speed ( e.g. Lanchester balancer (Fig. 2)).

Another possibility to achieve a perfect mass balance (and not only approximately) is to use two counter-rotating crankshafts, as for example with the H-engine .

## table

Number of cylinders Free forces
(1st order)
Free forces
(2nd order)
Free moments
(1st order)
Free moments
(2nd order)
Firing intervals for four-stroke engines
1 2 3 - - 720 °
2 row (180 °) 0 2 2 0 180 ° / 540 °
2 twin (360 °) 2 3 0 0 360 °
2 (V 90 °) 1 3 - - 270 ° / 450 °
2 (V 60 °) 2 3 - - 300 ° / 420 °
2 (boxer) 0 0 2 3 360 °
3 (row 120 °) 0 0 2 3 240 °
4 (row) 0 3 0 0 180 ° / 180 ° or 270 ° / 90 °
4 (V 90 °) 1 0 3 2 0 90 ° / 270 °
4 (Boxer 180 °) 0 0 0 2 180 ° / 180 °
5 (row) 0 0 2 2 144 ° / 144 °
6 (row) 0 0 0 0 120 ° / 120 °
6 (V 90 °) 1 0 0 3 3 150 ° / 90 ° or 120 ° / 120 ° (crank pin offset by 30 °)
6 (V 60 °) 1 0 0 3 3 120 ° / 120 ° (crank pin offset by 60 °)
6 (boxer 120 °) 0 0 1 2 120 ° / 120 °
8 (V 90 °) 0 0 1 0 90 ° / 90 ° /
12 (V 60 °) 0 0 0 0 60 ° / 60 °

Legend: 0 = fully balanced 1 = fully balanced 2 = partially balanced 3 = not balanced

1 Four- and six-cylinder V-engines (except racing engines) are usually designed with staggered crank pins so that the ignition intervals are the same.

## Uneven movements

### Rotational irregularity

Since reciprocating piston engines do not run continuously like turbines , but go through a process divided into different cycles, there is a speed and torque pulsation on the crankshaft that fluctuates around a stationary mean value (Fig. 3).

Fig. 3: Moment pulsation and rotational irregularity

The shape of the torsional irregularity is determined by the number of cylinders, the pressure curve in the cylinder, the geometry and the mass of the engine components as well as the working process (e.g. two-stroke or four-stroke process ) and the operating point (load / speed) of the engine. The power take-off z. B. a camshaft and the secondary drive of ancillaries can also have an influence.

This so-called rotational non-uniformity is the cause of torsional vibrations in the downstream drive train , which often lead to unpleasant engine noises . To reduce this, dual mass flywheels or torsional vibration absorbers or dampers are used. A converter transmission also dampens the shocks.

### Piston stroke and compression

The articulated connecting rod technology and other methods of achieving a variable crank drive should, among other things, control the compression ratio and course.

## literature

• Richard van Basshuysen; Fred Schäfer: Handbook Internal Combustion Engine Basics, Components, Systems, Perspectives . Wiesbaden: Vieweg, 3rd edition 2005, ISBN 3-528-23933-6 .
• Eduard Köhler: Internal combustion engines. Engine mechanics, calculation and design of the reciprocating engine. Wiesbaden: Vieweg, 3rd edition 2002, ISBN 3-528-23108-4 .