20 Modes of vibration, natural frequency, forcing frequency and resonance

Engine balance



39



2.5



2.0



T



1.5



1.0



0.5



0

0



1



2



3



4



F



5



6



7



f



Fig. 2.13 Transmitted vibration



likely to be needed to take the various static and transient loads enumerated

above. Road shock loads, for instance, may greatly exceed the dead weight.



2.21



Principal axes of inertia



If a long, fairly regular object, such as a potato or a lump of firm plasticine,

is pierced with a knitting needle in the general direction of its greatest

length, an axis of rotation may be obtained about which the moment of

inertia is small compared with those about axes generally at right angles to

it.

There is a particular axis, passing through the mass centre, about which,

owing to the general proximity of all the mass particles, the moment of

inertia is a minimum for the solid. This is one of the principal axes. The two

others, also passing through the mass centre, complete a trio of mutually

perpendicular principal axes. Of the second and third axes, one will be the

axis of maximum inertia and the other will have an intermediate value.

These three principal axes, which may be described in reference to a power

unit as the axes of natural roll, pitch and yaw, are the axes about which

torsional oscillation can be initiated without introducing lateral or translational

forces, and are the axes about which the mass, if supported in a homogeneous

elastic medium (such as soft rubber or jelly) and with gravitational forces

balanced, would take up component rotations when disturbed by any system

of applied torques.



2.22



Importance in the design of engine mountings



These principal axes are important in the design of engine mountings,

particularly the fore-and-aft ‘roll’axis, which ordinarily lies at an angle of 15

to 30° with the crankshaft axis, sloping downwards from front to rear as

indicated in Fig. 2.14. Ideally, the mountings should be disposed as to confine

rotation to this axis, so that torsional vibrations may be constrained without



40



The Motor Vehicle



introducing lateral forces. If rotation about any other axis is imposed by the

mountings, such lateral forces will arise, and may require additional constraints.

It will be noticed that, assuming lateral symmetry, the principal axis intersects

the crankshaft axis near the centre of the flywheel housing, so that mountings

placed on the sides of the housing could deal with torsional vibrations about

the principal axis as well as with direct ‘bump’ loads. The front mounting

would be placed high, as near to the principal axis as possible, and would

take the balance of the bump loads as determined by the position of the mass

centre. In the Chrysler mounting shown in Fig. 2.15, all reactions are distributed

between the front and rear mountings, snubbers only being provided at the

flywheel housing.

Figure 2.14 also indicates the centre of percussion, CP. The position of the

CP is determined by the destribution of the mass relative to the rear suspension

or pivot point, which in effect is the centre of suspension, CS. Usually it will

lie near the central transverse plane of the engine, which is the plane in

which the resultant of the unbalanced secondaries in a four-cylinder engine

acts. If CP can be located exactly in this plane by suitable choice of CS and

mass distribution, and if the front mounting can also be so placed, there will

be neither pitching moment due to the secondary disturbing force nor reaction

at the CS. The principle is similar to that applicable to a door stop, which

should be positioned at the centre of percussion so that, if the door is suddenly

blown open against it, the hinges are not overloaded.

In practice, it is rarely possible to arrange for exact coincidence as described

above, but the central plane is a structurally desirable, though not always



A



Z

A



CP



M



CS



Fig. 2.14 Principal axes



M



Fig. 2.15 Chrysler engine mounting



Z



Engine balance



41



convenient, location for the front mountings. These are indicated at AA in

Fig. 2.14, widely spaced to deal with torsional vibrations about the axis ZZ.

This percussion system appears to be an ideal means of dealing with

pitching disturbances; road shocks and cornering loads would be shared by

the attachments at CS and AA in a ratio determined by the position of the

mass centre M.A V arrangement of links with rubber-bonded bushes, with

the link centre lines meeting on the principal axis and so utilising the principle

of the instantaneous centre may be used, or else a type of front V-mounting

of ‘compression-shear’ units.

The arrangement used for the mounting of the three-cylinder Perkins

diesel engine in a light van chassis is shown in Fig. 2.16.

Both vertical and horizontal primary out-of-balance couples are present

in this engine, and to obtain insulation against these as well as the 1 1 order

2

torque harmonic a suspension giving a high degree of rotational flexibility

about all axes was needed. This was achieved by a V arrangement of sandwich

mountings very close to the centre of gravity (or mass centre), the front

rubber sandwich mounted so that its compression axis passes appproximately

through the centre of gravity. The degree of insulation obtained is excellent.

Engine movement under shock torque reaction, and when passing through

resonance on starting and stopping, is quite large, but has not proved

troublesome. A pair of circular sandwich units pitched to give greater torque

control may be used at the front instead of the rectangular form.

A great variety of rubber-to-steel bonded units to provide the many different

constraints required has been produced by Dunlop Polymer and a few are

shown in Fig. 2.17. The illustration includes early unbonded cushions, bonded

double shear and compression-shear mountings, a bonded eccentric bush,

rubber steel compression spring, and others.

It is possible to design units capable of resisting various combinations of

compression, shear and torsional loads, with appropriate variation in the

elastic properties of the rubber obtained by a suitable mix.

Though no mathematical treatment has been attempted here, the reader

will have realised that for quantitative analysis of inertias, modes of motion

and vibration frequencies, advanced and difficult mathematics are required,

combined with experimental measurement.



Buffers



Fig. 2.16 Perkins P-3 mounting



Interleaved

rectangular

mounting



42



The Motor Vehicle

Engine bracket



Engine foot



Chassis

bracket



Chassis member



Chassis



Engine



Engine



Rebound buffers and

precompression unit



Chassis



Fig. 2.17 Metalastik elastic engine mountings by Dunlop Polymer



Similar principles apply to transversely mounted engines, but an additional,

and very important, factor has to be taken into consideration. It is that,

because the gearbox and final drive are combined and mounted either on or

in the engine, the torque the mountings have to react is the engine torque

increased by the overall ratio of the final drive and gear engaged at any

particular time, instead of just that from the engine and gearbox alone. In

other words, it is between about 2 1 and 3 1 times as great. In the early days

2

2

of transverse engine installation, the solution was to allow the engine relatively

free vertical motion, within limits, while restricting the fore-and-aft motion

of the lower mountings and introducing a horizontal link, with pivot eyes at

its ends, to tie the top of the crankcase to the dash. This of course enables the

torque reaction to be taken between the top link and bottom mountings.

Later, extra steel link was obviated by building resistance to horizontal

movement into the rear high mounting, by either stiffening its rubber elements

against deflection in that direction or incorporating in it stops designed to

limit such movement progressively. A typical transverse engine mounting

system is that of the Rover 200 range, illustrated in Fig. 2.18. For a more

detailed treatise, the reader is recommended to the book Fundamentals

Balancing, by W. Thomas, published by the Institution of Mechanical

Engineers.



2.23



Hydraulically damped engine mountings



The previous sections have covered the basic considerations relating to the

classic designs. In recent years, however, following the advent of computer

aided design, it has become possible to solve much more complex problems

and to take into consideration larger numbers of variables. Consequently,

although hydraulic damping adds significantly to the costs of engine mountings,

it is being introduced on some of the up-market range of cars. In addition

to the six degrees of freedom, vertical bounce, and the lateral and longitudinal

modes, together with the three torsional modes, namely yaw, pitch and roll,

we can now take into account and cater for road wheel inputs and forces due

to uneven firing. The last mentioned, of course, are particularly prominent in

diesel engines.



Engine balance



43



Fig. 2.18 Three-point mounting system for the transversely installed engines of the

Rover 200 Series. All three are very flexible vertically but, for reacting final drive

torque, their motion is limited by their metal housings. The lower mounting on the

right in this illustration also limits movement of the engine parallel to the crankshaft



Freqencies of the disturbing forces are, of course, important considerations

in the successful design of hydraulically damped mountings. For an engine

with a speed range of 750–6000 rev/min, the secondary forcing frequency is

in the range 25–200 Hz. The magnitude of the force increases with the

square of the speed, as also does the acceleration of the engine, and therefore

the reaction due to its inertia, in the direction of the force. Consequently, the

amplitude of vibration over most of the speed range is constant.

With diesel engines, uneven firing generates strong forces of half and first

order, which are superimposed upon those of second order. So, for an engine

idling at 750 rev/min, the forcing frequencies are 6.25, 12.5 and 25 Hz. With

a six degree freedom system, this presents severe problems that can best be

solved by introducing hydraulic damping.

For isolation of the power unit at 25–200 Hz, its natural frequency should

be between 6 and 12 Hz. The forces are in one direction and generally

predominantly vertical, so it is not absolutely essential to have frequencies

for the other modes of vibration as low as 10 Hz. In most instances, therefore,

it is generally adequate if all modes are below 20 Hz, except for the bounce

mode, which should be between 8 and 10 Hz.

Although the frequencies of the second order forces are generally above

that of resonance of the system, they may be of magnitudes large enough to

generate high levels of vibration of the engine. At these frequencies,



44



The Motor Vehicle



20–30 Hz, the amplitude is limited, as previously indicated, by the inertia

due to the mass of the engine, although soft mountings are necessary. Even

so, idle shake can still be caused by resonance of components such as the

steering column or dash fascia.

The natural frequency of the engine mountings is in the same range as the

road wheel inputs, which are generally below 30 Hz, and which therefore

can cause engine shake. As a result, the occupants of the vehicle may have

the impression that the ride is poor. With diesel engines, half and first order

firing forces can cause idle shake. The way to control both of these forms of

shake is to introduce extra damping into the engine mountings.

One should be aware, however, that, because damping increases the hardness

of the mounting, this can adversely affect interior noise levels. In the range

from 30 to 300 Hz, the lower the stiffness of the mounting, the lower will be

the noise levels. On the other hand, for controlling shake in the 5–30 Hz

range, the damping should be as high as practicable. Consequently, hydraulically

damped mountings are usually designed to be effective in the lower frequency

range. Figure 2.19 shows the characteristics of a simple conical rubber mounting

produced with rubbers having different damping characteristics. In Fig. 2.20

the low frequency and, in Fig. 2.21, the high frequency characteristics of the

Avon Hydramount are shown.



Dynamic stiffness

Static stiffness



4



Test amplitude - dynamic stiffness ± 1 mm

Loss angle ± 1 mm at 10 Hz

High damped, 10° loss angle



3



Medium damped, 6° loss angle



2

Lightly damped, 2° loss angle



1

20



60



100

140

Frequency, Hz



180



220



Fig. 2.19 Typical characteristics of a typical Avon rubber mounting



Dynamic stiffness

Static stiffness



3

2

1



0

50



100

150

Frequency, Hz



200



Fig. 2.20 Low frequency characteristics of Hydramount



Engine balance



45

500



50



400



40

Stiffness

30



300



20



200



10



Dynamic Stiffness, N/mm



Damping loss angle, deg



Damping



100



0



0

0



4



8

12

Frequency, Hz



16



20



Fig. 2.21 High frequency characteristics of Hydramount



Testing is usually done at an amplitude of ±1 mm at 5–30 Hz and

±0.1 mm at 30–200 Hz. Noise transmission is mostly at amplitudes of less than

0.1 mm, whereas shake is generally at high amplitudes of 0.3 mm or more.



2.24



The Avon Hydramount



Hydramounts are designed to suit each installation, and therefore vary in

detail according to the vehicle to which they are applied. A typical example

is illustrated in Fig. 2.22. Its top cover comprises a conventional conical

rubber mounting crowned by an axial fixing stud, and its base is dished to

house a hydraulic damper assembly clamped between the two. This assembly

includes two diaphragms, the uppermost being clamped between upper and

lower snubber plates, both of which are perforated so that they do not impede

motion of the diaphragm other than to prevent it from being overstretched.

As can be seen from the illustration, the upper snubber plate is on top of

a dished partition, thus closing it and sealing within it the upper diaphragm

and its lower snubber plate. The space between the upper diaphragm and the

dished partition is filled with air, and vented to atmosphere. Apart from this

air space, the whole of the volume between the conical rubber mounting and

a bellow, or convoluted diaphragm, is filled with hydraulic fluid. The hydraulic

chamber above the air chamber contains the working fluid, while that below

is a reservoir.

Deflection of the conical rubber element pumps hydraulic fluid back and

forth through the damping orifice between the upper and lower chambers.

The volume of fluid transferred depends upon not only the amplitude of the

vibration and the size of the orifice, but also on the stiffness of the upper

diaphragm, its area and the travel between the upper and lower snubber

plates. If, however, the amplitude of movement is such that all the fluid

displaced is accommodated only by the deflection of the diaphragm, the



46



Main element



The Motor Vehicle



Snubber plate



Diaphragm

Air vent



Snubber

plate



Damping

passage



Air space

Bellow



Fig. 2.22 In the Avon Hydramount, there is an air chamber between the upper and

lower diaphragms, but the rest of the space between the top conical rubber element

and the lower, convoluted, diaphragm is filled with hydraulic fluid



dynamic stiffness of the mounting will be mainly that of the conical element.

That contributed by the diaphragm will be very small.

If the amplitude of motion increases, the diaphragm snubs out against the

lower perforated plate and fluid transfer, and hence damping, is introduced.

When the upper diaphragm has seated completely on the snubber plate, there

can be no more fluid transfer, so further deflection can be accommodated

solely by the conical rubber element. It follows that the Hydramount is an

amplitude-sensitive device. It is generally designed so that for amplitudes of

less than ±2 mm it has low stiffness and, at larger amplitudes, high damping.



Chapter 3



Constructional details of the

engine

From the outline of the general principles in Chapter 1, and the requirements

as regards balance in Chapter 2, we now turn to the details of construction,

leaving engines having six or more cylinders to Chapter 4. Sleeve valve,

rotary valve, and rotary piston engine constructions will then be dealt with

in Chapter 5.

The conventional layout described in Section 1.10 has become firmly

established, despite attempts to develop for automotive applications others

such as the swash-plate motor, widely used for hydraulic power, and the

Stirling engine, the relatively large size and weight of which virtually rules

it out. The gas turbine, while well established for large power units operating

mainly at constant speeds, has so far defied attempts to develop it in sizes

small enough and of adequate flexibility for quantity production for automotive

applications.

Because the reciprocating piston type has had the benefit of so much time,

effort and money spent continuously on its intensive development over

the century or more since its invention, prospects are indeed remote for a

successful challenge from any alternative power unit. Moreover, to justify

the abandonment of the world’s huge capital investment in plant and equipment

for its production, the potential for gain would have to be of truly major

significance. Another factor is the very large infrastructure that has been

built up, again worldwide, in terms of both experience and equipment for the

maintenance of such engines.



3.1



General engine parts



What may be classified as ‘general’ engine parts will first be described,

followed by the poppet valve and its various possible positions and methods

of operation. General cylinder construction, which depends on the location

of the valves, will follow and, finally, descriptions of typical four-cylinder

engines will be given.



3.2



The piston



The piston performs the following functions—

47



48



The Motor Vehicle



(1) Forms a movable gas-tight plug to confine the charge in the cylinder

(2) Transmits to the connecting rod the forces generated by combustion of

the charge

(3) Forms a guide and a bearing for the small end of the connecting rod,

and takes the lateral thrust due to the obliquity of that rod.

For the designer, the major problem is catering for the variation in operating

temperatures – from starting from cold at sub-zero to maximum output in

tropical climates, as well as the smaller, yet still large, variations encountered

in any one locality. Additionally, the weight of the piston must be kept to a

minimum to reduce vibration and the inertia loading on bearings, and to

avoid friction and other losses entailed in accelerating the pistons in both

directions. Consequently, although cast-iron pistons have been employed, to

minimise the effects of differential expansion between the piston and cylinder,

these are now found only in a few two-stroke engines. This is because of

their superior resistance to the higher temperatures generated in that cycle,

especially adjacent to the exhaust ports.



3.3



Thermal considerations



Almost all modern engines have aluminium alloy pistons. Because the

aluminium alloy is of lower strength than cast iron, thicker sections have to

be used so not all the advantage of the light weight of this material is

realised. Moreover, because of its higher coefficient of thermal expansion,

larger running clearances have to be allowed. On the other hand, the thermal

conductivity of aluminium is about three times that of iron. This, together

with the greater thicknesses of the sections used, enables aluminium pistons

to run at temperatures about 200°C lower than cast-iron ones. Consequently,

there is little or no tendency for deposition of carbon – due to thermal

breakdown of lubricant – beneath the piston crown or in ring grooves. So

important is this that sections thicker than necessary for carrying the mechanical

loads are in many instances used to obtain a good rate of cooling by heat

transfer.

The thermal flow in a piston is from the crown, out to the ring belt,

whence the heat is transferred through the rings to the cylinder walls and

thence to the coolant. A small proportion is transferred down to the skirt and

then across the bearing surfaces – between the skirt and cylinder walls – but

this is not of such great significance, partly because of the relative remoteness

of the skirt from the source of heat and partly its fairly light contact with the

cylinder walls. Some heat is also taken away with the lubricant but, again,

this is not a very significant proportion unless the underside of the crown is

positively cooled by a jet of oil or some other system. Highly-rated engines

– for example, some turbocharged diesel units – as well as engines with large

diameter pistons and those operating on the two-stroke principle, may have

oil-cooled pistons.



3.4



Design details



Some typical pistons for heavy-duty engines are illustrated in Figs 3.1 and

3.2. From Fig. 3.1, it can be seen that thick sections are used and there are

no abrupt changes in section which could form barriers to heat flow. The aim



Constructional details of the engine



Fig. 3.1



49



Fig. 3.2



has been not only to keep local temperatures below the level at which the

mechanical properties of the material begin to fall off significantly but also

to maintain fairly uniform thermal gradients to avoid thermal fatigue cracking,

especially adjacent to exhaust valves.

In Fig. 3.2 is illustrated a multi-piece oil-cooled piston, which may have

either a forged steel or a Nimonic crown. Oil in this instance is taken up an

axial hole in the connecting rod and, through a spring-loaded slipper pickup, into the space between the crown and skirt portions. It drains back

through holes not shown in the illustration. With this design, the two parts

are secured together by set-bolts inserted from above, so the crowns can be

removed for attention in service without disturbing the remainder of the

reciprocating assembly.

For light duty engines it used to be common practice to employ pistons

the skirts of which were split by machining a slot up one side. The object was

to enable the cold clearance between skirt and cylinder bore to be reduced

without risk of seizure when hot. Later, as ratings increased, T-shaped slots,

as illustrated in Fig. 3.3 were used, the head of the T exercising an influence

over thermal flow as well as on the resilience of the skirt under radial

compressive forces. Nowadays engines are generally too highly rated for Tslotted skirts. The modern equivalent is the piston with slots machined through

the base of its bottom ring grooves. In some instances, the ends of these

extend a short distance downwards, as in Fig. 3.4 which shows the Hepolite

W-slot piston.

More highly-rated engines, on the other hand, have no slots, being of

what is termed the solid skirt type. In many instances, these have steel

A



A



B

F

C



E

D



E



C

D



Fig. 3.3 Early light alloy piston