The compression and extension forces exerted by a damper at a given speed in or out are, as an empirical fact of life, highly unequal. Typically the extension force is three to four times the compression force. In terms of the mean force Fm, the extension and compression forces FE and
FCat a given speed magnitude are
FE¼ ð1 þ eDÞFm
FC¼ ð1 eDÞFm
where eDis the damper force transfer factor for that particular speed. Given the actual forces FEand
FC, the mean force Fmand the transfer factor eDmay be calculated from
Fm¼ FEþ FC 2 eD¼ FE FC 2Fm
Figure 3.12.4 Optimum damper characteristics. Reproduced from Fukushima, Hidaka and Iwata (1983) Optimum characteristics of automotive shock absorbers under various driving conditions and road surfaces, JSAE Review, pp.62–69.
The transfer factor (asymmetry factor) varies considerably with particular dampers and with the operating speed, but is typically 0.5–0.6. In general, the value is positive (greater extension damping), but eD¼ 1 would be pure compression damping. A value of eD¼ 0 is symmetrical damping, and eD¼ þ1
would be pure extension damping. On passenger vehicles, the rear dampers in particular may have great asymmetry. There is some indication that competition dampers, particularly in racing, may have less asymmetry. One possible explanation is that the greater bump damping, although less comfortable, gives a better road feel to the driver. This has also been found on competition motorcycles.
The scientific research literature is devoid of a good explanation of the asymmetry of dampers. The usual theoretical investigations of ride quality are symmetrical, so they are inherently unable to provide an explanation. However, the actual asymmetry has a very long history, going back to the original mechanical snubbers, which acted purely in extension, presumably for simplicity. Advertisements for early ‘shock absorbers’ included claims that the vehicle would be prevented from leaping out of potholes, perhaps because the wheel was prevented from drooping fully, perhaps because the snubber actually restrained the body upward movement.
The author has questioned various vehicle dynamicists informally on this point, and received less- than-convincing replies. Generally, there is a belief that there is a simple explanation, but this was not actually forthcoming. A typical explanation is that the problem is asymmetrical because ‘gravity acts downwards’, but the exact implications of this were not offered, although it is true that the body cannot accelerate downwards at more than 1 g. Admittedly this is an asymmetry, but in the usual ride quality studies this does not appear, because all ride motions are about the equilibrium position, and of limited amplitude. Suspension asymmetries such as rising rate springs, bump stops or droop stops, and damper asymmetry, are design consequences to be explained, they are not the cause. When the road is so rough and the suspension travel is so great that the workspace is exhausted, it could be exhausted equally at both ends, and the bump and droop stops could remain symmetrical.
An actual asymmetry arises naturally when the tyre normal force becomes significantly nonlinear, in effect when the wheel leaves the ground or when the bump is so severe that the tyre is fully compressed and the wheel rim is impacted. In the former case, at this point it does indeed become a significant factor that gravity acts downwards. However, a rim impact event is unusually severe, and such events are not the basis of normal ride or handling optimisation. Figure 3.13.1 shows a representative function for tyre vertical force against tyre deflection. Evidently, tyre deflection amplitudes exceeding the mean deflection are required to introduce asymmetry.
The total available range is about 70 mm, roughly in the ratio 1 extension to 4 compression, i.e. 14 mm extension before the tyre leaves the ground, but 56 mm compression before the tyre is crushed against the rim. Even within the linear stiffness model, the extension range of 10–15 mm acts as an asymmetrical limit. Hence, continuous short wave sinusoids of amplitude 10 mm, or ramp-steps up or down of that size, are symmetrical, of 15 mm are slightly asymmetrical and of 20 mm or more are highly asymmetrical. Relative to the mean tyre vertical force, the greatest downward force is only about 1/4 of the greatest possible upward force. This seems to offer some justification for relieving the damper compression force at high velocities, but not at low ones. This also suggests that perhaps long damper compression strokes should be pressure relieved, contrary to present thinking about stroke sensitive damping.
Figure 3.13.2 The effect of damper force transfer factor eD on vehicle body vertical acceleration when
driving on a rough road, simulation results. Reproduced from Fukushima, Hidaka and Iwata (1983) Optimum characteristics of automotive shock absorbers under various driving conditions and road surfaces, JSAE Review, pp.62–69.
Figure 3.13.3 The effect of damper force transfer factor eDon vehicle body vertical acceleration when driving
over a solitary positive bump, simulation results. Reproduced from Fukushima, Hidaka and Iwata (1983) Optimum characteristics of automotive shock absorbers under various driving conditions and road surfaces, JSAE Review, pp.62–69.
The tyre enveloping characteristic is said to be a factor here. The tyre can ride over a short hole to some extent, without necessarily maintaining contact with the bottom of the hole, but a short bump must penetrate the tyre profile fully. However, the tyre need not make contact with the full profile of a bump, it may miss the internal corners. Also, the argument would only apply to short steep bumps and holes.
Hypothetically, a further possible factor is that passenger sensitivity is not symmetrical, and that sharp upward and downward accelerations are not equally uncomfortable.
The study by Fukushima et al. (1983), addressing desirable damper characteristics, dealt with this to some extent, Figures 3.13.2 and 3.13.3. It is notable that for driving on a rough road they found no favourable effect for asymmetry. For driving over an upward bump they found, understandably, that asymmetry was desirable. They gave no result for a trough (negative bump).
To the author, the explanations given above, are tentative at best. It may be felt that there must be a physical explanation, but perhaps, not. The explanation may be being sought in the wrong place. It may simply be that asymmetry is more convenient for the damper manufacturer, or, to put it bluntly, it is cheaper to provide extension damping than to provide compression damping. This is basically because of the constructional characteristics of the telescopic hydraulic damper, which has more difficulty in providing large compression forces without risking cavitation.
A definite disadvantage of damper asymmetry is the resulting damper jacking. This is analysed in Section 7.15.
It appears, then, that the usual ride quality studies on low-amplitude random roads can seek to explain and to optimise the mean damping coefficient, but that the asymmetry factor must be sought elsewhere, amongst:
(1) tyre range asymmetry on large deflections; (2) road bump/trough asymmetry;
(3) passenger sensitivity asymmetry; (4) damper internal construction asymmetry; (5) tyre enveloping asymmetry;
(6) manufacturing costs.
Given a putative explanation (e.g. there are more holes than bumps), one must ask whether the removal of such a cause would result in future dampers being made symmetrical.
4.1 Introduction
The analysis of the vehicle presented in previous chapters, for example the heave-and-pitch motion, was based on the damping coefficient CWeffective at the wheel. However the damper itself is not
installed at this point, but elsewhere on the suspension. Often, for a car, it operates on the bottom suspension arm. Sometimes it operates through a linkage, including various forms of rocker, especially on racing cars and motorcycles. This chapter considers how to relate the damping characteristic at the wheel to the characteristics of the damper itself. This involves:
(1) evaluation of the relative motion of the wheel and damper; (2) consideration of the implications of this ratio.
The following sections therefore define the motion ratio, consider its consequences, and explain methods of evaluation for various kinds of suspension. An understanding of the analytical methods of analysis, such as the drawing of velocity diagrams, makes it possible to write a computer program to solve such problems, an instructing and interesting exercise in itself.
The damper free stroke is SF. The installed stroke, possibly limited by bump or droop stops, is SI.
The damper stroke utilisation is
UDS¼
SI
SF