122 Reasons for flexible mountings

It is the objective of flexible mounting design to cope with the many requirements, some having conflicting constraints on each other. A list of the duties of these mounts is as follows:

1 To prevent the fatigue failure of the engine and gearbox support points which would occur if they were rigidly attached to the chassis or body structure.

2 To reduce the amplitude of any engine vibration which is being transmitted to the body structure.

3 To reduce noise amplification which would occur if engine vibration were allowed to be transferred directly to the body structure.

4 To reduce human discomfort and fatigue by partially isolating the engine vibrations from the body by means of an elastic media.

5 To accommodate engine block misalignment and to reduce residual stresses imposed on the engine block and mounting brackets due to chassis or body frame distortion.

6 To prevent road wheel shocks when driving over rough ground imparting excessive rebound movement to the engine.

7 To prevent large engine to body relative movement due to torque reaction forces, particularly in low gear, which would cause excessive misalignment and strain on such components as the exhaust pipe and silencer system.

8 To restrict engine movement in the fore and aft direction of the vehicle due to the inertia of the engine acting in opposition to the accelerating and braking forces.

1.2.3 Rubber flexible mountings (Figs l.l0, l.ll and l.l2)

A rectangular block bonded between two metal plates may be loaded in compression by squeezing the plates together or by applying parallel but opposing forces to each metal plate. On compression, the rubber tends to bulge out centrally from the sides and in shear to form a parallelogram (Fig. l.l0(a)).

To increase the compressive stiffness of the rubber without greatly altering the shear stiffness, an interleaf spacer plate may be bonded in between the top and bottom plate (Fig. l.l0(b)). This interleaf plate prevents the internal outward collapse of the rubber, shown by the large bulge around the sides of the block, when no support is provided, whereas with the interleaf a pair of much smaller bulges are observed.

Fig. 1.10 (a and b) Modes of loading rubber blocks

When two rubber blocks are inclined to each other to form a 'V' mounting, see Fig. l.ll, the rubber will be loaded in both compression and shear shown by the triangle of forces. The magnitude of compressive force will be given by Wc and the much smaller shear force by WS. This produces a resultant reaction force WR. The larger the wedge angle O, the greater the proportion of compressive load relative to the shear load the rubber block absorbs.

The distorted rubber provides support under light vertical static loads approximately equal in both compression and shear modes, but with heavier loads the proportion ofcompressive stiffness

Fig. 1.11 'V'rubber block mounting

Deflection |m)

Fig. 1.12 Load-deflection curves for rubber block

Deflection |m)

Fig. 1.12 Load-deflection curves for rubber block to that of shear stiffness increases at a much faster rate (Fig. 1.12). It should also be observed that the combined compressive and shear loading of the rubber increases in direct proportion to the static deflection and hence produces a straight line graph.

1.2.4 Axis of oscillation (Fig. 1.13)

The engine and gearbox must be suspended so that it permits the greatest degree of freedom when oscillating around an imaginary centre of rotation known as the principal axis. This principal axis produces the least resistance to engine and gearbox sway due to their masses being uniformly distributed about this axis. The engine can be considered to oscillate around an axis which passes through the centre of gravity of both the engine and gearbox (Figs 1.13(a, b and c)). This normally produces an axis of oscillation inclined at about 10-20° to the crankshaft axis. To obtain the greatest degree of freedom, the mounts must be arranged so that they offer the least resistance to shear within the rubber mounting.

1.2.5 Six modes of freedom of a suspended body (Fig. 1.14)

If the movement of a flexible mounted engine is completely unrestricted it may have six modes of vibration. Any motion may be resolved into three linear movements parallel to the axes which pass through the centre of gravity of the engine but at right angles to each other and three rotations about these axes (Fig. 1.14).

These modes of movement may be summarized as follows:

Linear motions Rotational motions

1 Horizontal 4 Roll longitudinal 5 Pitch

2 Horizontal lateral 6 Yaw

3 Vertical

1.2.6 Positioning of engine and gearbox mountings (Fig. 1.15)

If the mountings are placed underneath the combined engine and gearbox unit, the centre of gravity is well above the supports so that a lateral (side) force acting through its centre of gravity, such as experienced when driving round a corner, will cause the mass to roll (Fig. 1.15(a)). This condition is undesirable and can be avoided by placing the mounts on brackets so that they are in the same plane as the centre of gravity (Fig. 1.15(b)). Thus the mounts provide flexible opposition to any side force which might exist without creating a roll couple. This is known as a decoupled condition.

An alternative method of making the natural modes of oscillation independent or uncoupled is achieved by arranging the supports in an inclined 'V' position (Fig. 1.15(c)). Ideally the aim is to make the compressive axes of the mountings meet at the centre of gravity, but due to the weight of the power unit distorting the rubber springing the inter-section lines would meet slightly below this point. Therefore, the mountings are tilted so that the compressive axes converge at some focal point above the centre of gravity so that the actual lines of action of the mountings, that is, the direction of the resultant forces they exert, converge on the centre of gravity (Fig. 1.15(d)).

The compressive stiffness of the inclined mounts can be increased by inserting interleafs between the rubber blocks and, as can be seen in Fig. 1.15(e), the line of action of the mounts converges at a lower point than mounts which do not have interleaf support.

Engine and gearbox mounting supports are normally of the three or four point configuration. Petrol engines generally adopt the three point support layout which has two forward mounts (Fig. 1.13(a and c)), one inclined on either side of the engine so that their line of action converges on the principal axis, while the rear mount is supported centrally at the rear of the gearbox in approximately the same plane as the principal axis. Large diesel engines tend to prefer the four point support

(a} Lo n gitud i n a 11 y mou nted powâ r u r»it with three point support (petrol engine)

(a} Lo n gitud i n a 11 y mou nted powâ r u r»it with three point support (petrol engine)

Fig. 1.13 Axis of oscillation and the positioning of the power unit flexible mounts

arrangement where there are two mounts either side of the engine (Fig. 1.13(b)). The two front mounts are inclined so that their lines of action pass through the principal axis, but the rear mounts which are located either side of the clutch bell housing are not inclined since they are already at principal axis level.

1.2.7 Engine and transmission vibrations

Natural frequency of vibration (Fig. 1.16) Asprung body when deflected and released will bounce up and down at a uniform rate. The amplitude of this cyclic movement will progressively decrease and the number of oscillations per minute of the rubber mounting is known as its natural frequency of vibration.

There is a relationship between the static deflection imposed on the rubber mount springing by the suspended mass and the rubber's natural frequency of vibration, which may be given by

Fig. 1.14 Six modes of freedom for a suspended block

where «0 = natural frequency of vibration (vib/min)

x = static deflection of the rubber (m)

This relationship between static deflection and natural frequency may be seen in Fig. 1.16.

Resonance Resonance is the unwanted synchronization of the disturbing force frequency imposed by the engine out of balance forces and the fluctuating cylinder gas pressure and the natural frequency of oscillation of the elastic rubber support mounting, i.e. resonance occurs when

disturbing frequency natural frequency

Fig. 1.16 Relationship of static deflection and natural frequency

Transmissibility (Fig. 1.17) When the designer selects the type of flexible mounting the Theory of Transmissibility can be used to estimate critical resonance conditions so that they can be either prevented or at least avoided.

Transmissibility (J) may be defined as the ratio of the transmitted force or amplitude which passes through the rubber mount to the chassis to that of the externally imposed force or amplitude generated by the engine:

where

Ft Fd transmitted force or amplitude imposed disturbing force or amplitude

This relationship between transmissibility and the ratio of disturbing frequency and natural frequency may be seen in Fig. 1.17.

[d) Converger! mount geometry

Fig. 1.15(a-e) Coupled and uncoupled mounting points

The transmissibility to frequency ratio graph (Fig. 1.17) can be considered in three parts as follows:

Range (I) This is the resonance range and should be avoided. It occurs when the disturbing frequency is very near to the natural frequency. If steel mounts are used, a critical vibration at resonance would go to infinity, but natural rubber limits the trans-missibility to around 10. If Butyl synthetic rubber is adopted, its damping properties reduce the peak transmissibility to about 232. Unfortunately, high damping rubber compounds such as Butyl rubber are temperature sensitive to both damping and dynamic stiffness so that during cold weather a noticeably harsher suspension of the engine results.

Damping of the engine suspension mounting is necessary to reduce the excessive movement of a flexible mounting when passing through resonance, but at speeds above resonance more vibration is transmitted to the chassis or body structure than would occur if no damping was provided.

Range (II) This is the recommended working range where the ratio of the disturbing frequency to that of the natural frequency of vibration of the rubber mountings is greater than 132 and the trans-missibility is less than one. Under these conditions off-peak partial resonance vibrations passing to the body structure will be minimized.

Range (III) This is known as the shock reduction range and only occurs when the disturbing frequency is lower than the natural frequency. Generally it is only experienced with very soft rubber mounts and when the engine is initially cranked for starting purposes and so quickly passes through this frequency ratio region.

Example An engine oscillates vertically on its flexible rubber mountings with a frequency of 800 vibrations per minute (vpm). With the information provided answer the following questions:

a) From the static deflection-frequency graph, Fig. 1.16, or by formula, determine the natural frequency of vibration when the static deflection of the engine is 2 mm and then find the disturbing to natural frequency ratio. Comment on these results.

b) If the disturbing to natural frequency ratio is increased to 2.5 determine the natural frequency

Fig. 1.17 Relationship of transmissibility and the ratio of disturbing and natural frequencies for natural rubber, Butyl rubber and steel

of vibration and the new static deflection of the engine. Comment of these conditions.

Vx V0-002 30

0.04472 n 800

670.84 vib/min

1.193

The ratio 1.193 is very near to the resonance condition and should be avoided by using softer mounts.

30 320

= 0.008789m or 8.789mm

A low natural frequency of 320 vib/min is well within the insulation range, therefore from either the deflection-frequency graph or by formula the corresponding rubber deflection necessary is 8.789mm when the engine's static weight bears down on the mounts.

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