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From Spoon Brakes to Two Leading Shoes

5th February 1943
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Page 20, 5th February 1943 — From Spoon Brakes to Two Leading Shoes
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Which of the following most accurately describes the problem?

Deceleration and Weight Transference from the Design Angle. Although Modern -Brqkes are Excellent, There is Scope for the Disc Type

pRACTICAL braking problems and the design of various systems were the main subjects which I reviewed in a previous article. (This appeared in our issue dated January 29.) Now I propose to explain what may be described as external factors, and to deal with some of the simple mathematict principles involved.

No matter how powerful and efficient the brakes may be, the controlling factors in stopping a Nehicle lie outside them. Braking, assuming that sufficient pressure be applied at the drums to give the deceleration required, is dependent on the load on the wheels and the coefficient of friction between the tyres and the road. By experiment this coefficient of friction has been established at an average figure of 0.7, but conditions are often met with .vliere it is above unity and sometimes as low as 0.2.

The aim of chassis designers—with a feW, exceptions— is a braking efficiency of 100 per cent., which gives a deceleration equal to " g " or 92,2 ft. per sec, per sec. This figure is obtainable only when the coefficient of friction between the tyre and the road is equal to, or exceeds,_ unity, as can be seen from the following formulm:— Retarding Force = Vehicle Weight x Deceleration + g.

If the deceleration is to equal g, the retarding force must be equal to the weight of the vehicle, but the adhesion between the tyre and the road, which controls skidding, is dependent on the coefficient of friction, as follows:— Adhesion = Vehicle weight x Coefficient of friction. Therefore, the coefficient of friction must be equal to, or must exceed unity, to give the desired 'retardation.

It has been found possible to obtain 100 per cent. braking efficiency on vehicles weighing up to approximately 2 tons gross, but for heavier types a 60 per cent, efficiency, or retardation of 19.92 ft. per.sec. per sec. is the maximum obtainable except under very favourable conditions.

A Questionable Safety Theory

Among p.s.v. operators I have 'met. some who argue that an efficiency of not more than 40 per cent, is desirable on the ground that a skidding bus is dangerous to passengers, pedestrians and Other road users alike and that the speeds of locally operated passenger vehicle are low enough for 40 per tent. efficiency to be_satisfactory. This, however, does not appear to take into account the probability that the vehicle just ahead has better than 40 per cent. retardation efficiency.

When the brake linkage is being considered, it is necessary to know, or to assume, all the conditions under which the vehicle is to operate. A value must be determined for the coefficient of friction between tyres and road, the retardation to be aimed at must be decided, and, from -the latter, the weight transference to the front axle under maximum braking conditions must be calculated. It is important to note, however, that all strength calculations for the various parts of the system must: be based on a coefficient of friction of unity, because that figure can, be, and often is, reached.

The braking effort to stop a wheel is directly propor

tional to the load carried and is not equal on all the wheels, of a vehicle. During braking the load tends to move forwards towards the front axle. The weiglat transference on to the front axle, due to this tendency, is given by the

following formula:— LxGxa Weighttransference — where L is the total weight of' the vehicle, acting at its centre of gravity, G the height of the centre of gravity from the ground, a the deceleration, W the wheelbase, and g the deceleration due to gravity. • It follows that the braking effort on the front and rear axles is not decided by the static loads on them but by • the static loads plus the dynamiC loads set up by deceleration. Further, the additional dynamic lbad given by the formula is not dependent on the 'longitudinal pesition of the centre of gravity but solely On its height from the ground, although the static weight distribution between the axles does depend ou the longitudinal position. Consequently, two vehicles of identical wheelbase and • with the same gross weight, but differing in that one has nermal and the other forward control, will require different braking efforts on their respective front and rear axles.

An example is worked below to show the steps necessary to obtain the brake leverages to both axles of a four! wheeled lorry of gross weight 12 tons for 60 per cent. braking efficiency. Fig. 5 gives the chassis dimensions required.

0.6 • x g x 12' X 60 Weight transference — = 3 tons.

g x 144 Static weight distribution is 4-tons front, 8 tons rear. Dynamic weight distribution is 7 tons front, 5 tons rear. As the braking effort is proportional to the load on the wheels the braking at the front should be seven-twelfths of the total, or 58.33 per cent. and that at the rear five-twelfths of the total, or 41.66 per cent. In round figures, then. a braking force equal to 60, per cent. of the total must be applied to the front Wheels and 40 per cent. to the rear. .

A vehicle. of this . size, would be provided with brakes having 16-in. or .161-in. drums. Assttming a coefficient"of friction between .tYre and road'of unity and a rolling radius of 20 ins, for the tyre, the force required ,at the front-brake drum face can be calculated from the formula given below.

Force = L, x a r,

where'll is the front-axle weight, a the percentage deceleration, •R th'e rolling. radius of the tyre and r the radius of the brake drum.

Accordingly, force = 7 x 0.6 x 20 8 = 10.5 tons.

In order to be able to calculate the leverage of the hook up, the leverage and the internal mechanical advantage of the brake unit must be known. Contrary to expectation these two figures are not, the same,the former being a combination of-a special factor, obtained experimentally

by the brake maker, and the mechanical advantage. This factor for the most powerful ordinary brakes (not twoleading-shoe brakes) is about 5 and includes the coefficient ofafriction between the shoes and the drum.

Assume, then, that the factor is 5 and the mechanical advantage inside the brake 8. This makes the internal levera,ge, for effort-calculation purposes, 40 to 1. ..4 Effort required at shoe tip = 10.5 40 = 0.2625 tons. With wedge operation and cable linkage, the pull required is increased, as the efficiency of the former is about 90 per cent, and that of the latter approximately 60 per cent.

0.2625 x 100 x 100 So the actual cable pull required — 90 x 60 tons = 0.485 tons for two wheels.

The available pedal effort is 200 lb., 7/12 of which is used for the front brakes, namely, 116.67 lb.

So the leverage = 0.485 x 2240 116.67 = 9.32 to 1. As the braking effort required at the rear wheels is 5/7 of that required at the front, the rear leverage will be 9.32 x 5 7 = 6.66 to 1.

Designing to Avoid Skids ,• A systematically designed brake hook-up of this. nature will not cause a front-Wheel skid under normal operating conditions, the graph (Fig. 7) showing exactly when skidding will occur on both front and rear wheels. When the braking effort at the periphery of. the tyre is equal to the adhesion between tyre androad the wheel is on the point of skidding. This equality is given at the 60 per cent.* braking aimed at for both wheels and occurs when the coefficient of friction is only 0.6.

There is a number of ways of linking the pedal to the brakes, the three most popular being hydraulic piping, cable, and cable and rod combined. Compressed air and all-rod book-ups aze not widely used on commercial vehicles, the former because of the rather higher cost and the extra parts involved (notably a compressor), and the iatter because of the difficulty experienced in connecting dthe oscillating wheels to a cross-shaft lever without interference with the brake operation.

This point is illustrated in Fig. 6, where point A represents the centre about which the spring oscillates. In order to find the centre about which the brake rod should revolve, a parallelogram is constructed as follows:—Join A to C (the middle of the top leaf of the spring at the axle centre line); from B (the centre of the brake-operatinglever eye on the axle) draw a line parallel to AC. Join B to C and from A draw a line parallel to BC to cut the line BD in D, which is the point required.

Should the rod be pivoted at any other point than D, say, E, the arc described by the spring centre, which is the same path as that of the axle, will be different, every time the springs deflect, from that described by the lever

eye, and the brakes, as a result, will be applied. .

The three popular linkages mentioned are all free from this disadvantage, the hydraulic system incorporating wheel connections of reinforced rubber tubing and the other two using flexible cables.

An interesting unit, for inclusion in the brake hook-up, is marketed by Bendix, Ltd., which concern claims that it gives differential braking. It consists of a pre-loaded spring and is inchicled as part of the rear-brake operating rod, usually at the cross-shaft end, its object being to provide braking force in the proportions demanded by vehicle speed, so as to reduce facing wear and to extend the period between brake adjustments. Were the unit incorporated in the linkage previously determined, the braking ratio of 60 per cerrt. front, and 40 per cent, real would not be used, a leverage to give 50/50 braking being substituted.

The spring rate is so arranged that all braking forces below those required for a deceleration of 12 to 14 ft. per sec. per sec., cause no extension in it, but above this figure the spring expands and absorbs part of the energy normally transferred to the rear wheels, thus decreasing the rear leverage to an extent which makes the ratio between front and rear 60 to 40. When maximum pedal pressure is applied to give maximum braking efficiency and consequently maximum Weight transference, no effort is removed from the front brakes, where all of it is required, but part is removed from the rear brakes, which makes the possibility of skidding more remote. Early types of brake were adjusted by the simple method of rotating the cam or toggle by shortening the effective length of the brake rod. Other systems, were used, but nearly all have been virtually superseded by the internal adjuster. This may consist of a wedge which is forced between the shoes and presses them outwards towards the brake drums, or of a leftand right-hand threaded device which aerves the same purpose but is actuated by a crown wheel and pinion. The crown wheel is rotated and turns the pinions which are integral with the adjuster screws operating in the adjuster housing. The recommended practice for adjusting brakes with either of these two mechanisms is to turn the adjusters until the liners are forced solidly against the drums and then to reverse the process and turn them back two notches. As the adjusters click when rotated it is a simple matter to gauge the two notches back, as these are merely represented by two clicks.

Many attempts have been made in the past to design an efficient brake adjuster 41 operate automatically. One of the most popular of these automatic adjusters is the R.P. Here the adjustment is carried out in the expander every time the pedal is depressed more than a certain distance, the amount being .pTeviously determined by observed facing wear.

In another scheme a mechanism is incorporated on the brake cross-shaft which similarly adjusts the brakes when a given clearance between shoe and drum is reached. Automatic adjusters must not be too, sensitive, because if the predetermined clearance were reached when the drums were hot, and the brakes were adjusted accordingly, then, when the drums cooled and 'contracted, the brakes would hind and might even become locked solid.

There can be no doubt that modern brakes are excellent and that, in their present form, there is little room for improvement, nevertheless, chassis designers have a corn

plaint that drum diameters are inconveniently big. It Would appear, therefore, that there is scope for experiment on brakes of smaller size with the'same 'efficiency as their larger counterparts. •

If present designs cannot be reduced in size, I suggest that, the little-known disc brake which already shows great promise should be developed further. It might well provide the solution to "Some of the chassis makers' difficulties.

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