Dynamic Stability of ThreeWheeled Vehicles in AutomotiveType…

12 Фев 2015 | Author: | No comments yet »
Mercedes-Benz F300 Life Jet

Dynamic Stability of

with three-wheeler contributions by


T he idea of smaller, energy-efficient for personal transportation seems to introduce the three wheel Opinions normally run either against or strongly in favor of the wheel layout. Advocates to a mechanically simplified chassis, manufacturing costs, and superior characteristics. Opponents decry the propensity to overturn. Both have merit. Three-wheelers are and less costly to manufacture. But poorly designed or in the wrong a three wheel platform is the forgiving layout. When designed, however, a three car can light new fires of enthusiasm tired and routine driving And today’s tilting three-wheelers, that lean into like motorcycles, point the way to a new of personal transportation products of lower mass, far greater economy, and superior cornering

Inherently Responsive Design

to the three-wheeler’s inherent characteristics can a high-performance machine that out corner many four-wheelers. A designed three-wheeler is likely to be one of the responsive machines one will experience over a winding Superior responsiveness is primarily due to the rapid yaw response time.

Yaw time is the time it takes for a to reach steady-state cornering a quick steering input. A sprung four-wheeler will a yaw response time of about seconds, and a four wheel car will respond in about that time. A well three-wheeler can reach steady-state in as little as 0.10 seconds, or 33 percent quicker than a four wheel car.

steering response has nothing to do the number of wheels or how they are It is a byproduct of reduced mass and low moment of inertia. A typical is lighter and has approximately 30 percent polar moment than a four wheel design. a link to video and driving on the new Morgan three-wheeler. which is a copy of the one built in the twenties and Notice that the vehicle’s wheels are located wide and the height is low. Location of the of gravity is crucial to a three-wheeler’s and rollover stability.

Rollover Stability of Conventional Three-Wheeler

A conventional, non-tilting wheel car can equal the rollover of a four wheel car, the location of the center-of-gravity (cg) is low and the side-by-side wheels. Like a wheel vehicle, a three-wheeler’s of safety against rollover is by its L/H ratio, or the half-tread (L) in relation to the cg (H). Unlike a four-wheeler, a three-wheeler’s half-tread is determined by the between the actual tread between the side-by-side wheels) and the location of the cg, which translates an effective half-tread. The effective can be increased by placing the side-by-side farther apart, by locating the cg to the side-by-side wheels, and to a lesser by increasing the wheelbase. Rollover increases when the effective is increased and when the cg lowered, of which increase the L/H ratio.

A way to model a three-wheeler’s margin of against rollover is to construct a cone using the cg height, its along the wheelbase, and the effective of the vehicle. Maximum lateral are determined by the tire’s friction Projecting the maximum turn-force toward the ground forms the of the cone. A one-g load across the vehicle’s cg, for example, result in a 45 degree projection the ground plane. If the base of the falls outside the effective the vehicle will overturn it skids. If it falls inside the half-tread, the vehicle will before it overturns. To see a drawing a base-cone illustration of single wheel (1F2R) and single wheel (2F1R) vehicles, on: Single Front Single Wheel Comparison (23k).

The foregoing is a simple rigid-body and it does not consider the effects of rebound, and body-roll inertial It therefore provides an approximation of threshold under dynamic

Oversteer/Understeer Characteristics

The single wheel layout naturally and the single rear wheel naturally understeers. Because degree of understeer is preferred in vehicles, the single rear layout has the advantage with the lay Another consideration is the effect of and accelerating turns. A braking tends to destabilize a single wheel vehicle, whereas an turn tends to destabilize a rear wheel vehicle. braking forces can reach magnitudes than acceleration (maximum braking force is by the adhesion limit of all three rather than two or one wheel in the of acceleration), the single rear design has the advantage on this Consequently, the single rear layout is usually considered the platform for a high-performance consumer in the hands of the non-professional driver. But drivers often prefer oversteer to understeer. Oversteer the skilled driver the ability to extreme maneuvers that an vehicle would simply through and refuse to perform. by varying tire size and a single front wheel can be designed for neutral steer oversteer present only at the of adhesion. Much depends on the of the design, as well as driver and skills.

Tilting Three-Wheelers

Tilting three-wheelers, vehicles lean into turns motorcycles, offer increased to rollover and much greater power — often that of a four wheel And designers are no longer limited to a low layout in order to obtain rollover stability. Allowing the to lean into turns a much greater latitude in the of a cg location and the separation between wheels.

Consider that a motorcycle has no wheels, yet it does not overturn going around corners. A negotiates turns by assuming a angle that balances the of forces resulting from the rate. The rider leans the into the turn so it remains in with the forces that are on it. As long as the motorcycle’s lean matches the vector of forces in a (resultant), it will not overturn. In to stay in balance with forces under all possible however, a motorcycle must be to lean at an angle of 50-55 before any part of the machine the ground.

Three and four vehicles can also be made to into turns. But with vehicles equipped with wheels, other physical and realities come into For example, a vehicle having a body may contact the ground at moderate lean angles, will make it impossible to in balance with turn at the upper extremes. In addition, the the separation between the side-by-side the greater the wheel movement at lean angles. The movement of the wheels can become excessive at relatively small angles of in vehicles having a track that of conventional automobiles. And the challenges of accommodating steering, and tilting, along with the limitations of CV joints on powered places additional limitations on the angle of tilting multi-track As a result, much of the recent on tilting suspension systems has the three wheel platform. The 32 Slalom (1F2R) and the Mercedes Life-Jet (2F1R) are excellent of modern tilting three designs.

Free-Leaning versus Lean Control

Tilting can be free-leaning and controlled by the rider, like ordinary motorcycles. if the mechanical limit of lean is than is necessary to balance forces under all possible then some form of (forced) lean control be used to account for turns exceed the lean limit. is usually accomplished by hydraulic or actuators operating on signals an electronic control unit Normally, the ECU processes signals sensors that monitor acceleration, vehicle yaw and lean steering angle, and other factors, then provides output to the lean actuators. advantage of active lean is that the operator is no longer to balance the vehicle, as when a motorcycle. With active control, the vehicle is driven like an ordinary automobile, and the control system takes of the rest.

Rollover Threshold of TTWs

The threshold of a TTW is determined by the same forces and geometric relationships determine the rollover threshold of vehicles, except that the of leaning become a part of the As long as the lean angle the vector of forces in a turn, just like a motorcycle, the has no meaningful rollover threshold. In words, there will be no projection of the resultant in turns, as is the with non-tilting vehicles. In a increasing turn, the vehicle lean at greater and greater as needed to remain in balance turn forces. Consequently, the of the track is largely irrelevant to stability under free-leaning With vehicles having a limit, however, the resultant begin to migrate outboard the turn rate increases the rate that can be balanced by the lean angle. Above limit, loads are transferred to the wheel, as in a conventional vehicle.

Foale, author of Motorcycle Design . explains the behavior of an TTW in terms of a virtual motorcycle located between the two opposing wheels. In a balanced turn, the remains in line with the motorcycle wheel. But in turns above the limit of lean, the projects to the outside of the virtual (vehicle centerline), according to the of turn forces in excess of at lean limit. It’s important to note that the cg moves inboard as the vehicle into a turn.

When calculating the rollover of a TTW having a lean limit, one consider the inboard migration of the cg due to the of lean, the outboard projection of at the friction limit of the tires, and the relationships between the cg height, the half-tread (at lean limit), and the

TTWs With Only One Wheel

Another interesting of TTWs includes vehicles only a single leaning such as the Lean Machine at General Motors in the late and early ’80s. GM’s Machine is a 1F2R design the single front wheel and compartment lean into while the rear section, carries the two side-by-side wheels and the train, does not lean. The two are connected by a mechanical pivot.

The threshold of this type of depends on the rollover threshold of of the two sections taken independently. The section behaves according to the base cone analysis. Its ratio determines its rollover Assuming there is no lean on the leaning section, it would as a motorcycle and lean to the angle for balanced turns. The height of the of gravity of the leaning section is as long as there is no effective limit.

The rollover threshold of a without an effective lean will be largely determined by the threshold of the non-leaning section. But the section can have a positive or effect, depending on the elevation of the axis at the point of intersection the centerline of the side-by-side wheels. If the axis (the roll of the leaning section) projects to the centerline at a point higher the center of the wheels, then it reduce the rollover threshold by the non-leaning section. If it projects to a that is lower than the of the side-by-side wheels, then the threshold will actually as the turn rate increases. In words, the vehicle will more resistant to overturn in turns. If the pivot axis to the centerline of the axle, then the section has no effect on the rollover established by the non-leaning section.

In vehicles of this type have a limit on the degree of rollover threshold would be as with an all-tilting-wheels vehicle at or above its limit of lean. In case, the cg height of the leaning would have an important on the behavior of the vehicle as a whole. a tilting vehicle reaches its of lean and locks against its stops, it can be analyzed as a non-tilting having the geometric configuration of the vehicle at lean limit.

The incline of the roll axis of the section is an important consideration this type of vehicle. free-leaning designs, the roll should project to the ground at the (leaning) wheel. This is to avoid a roll/lean couple, could result in roll during acceleration and braking. is not as important in vehicles equipped active lean control


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