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The spring rate or spring constant of a spring is the change in the force it exerts, divided by the change in deflection of the spring. Vehicles which carry heavy loads will often have heavier springs to compensate for the additional weight that would otherwise collapse a vehicle to the bottom of its travel stroke.
Heavier springs are also used in performance applications where the loading conditions experienced are more extreme. Springs that are too hard or too soft cause the suspension to become ineffective because they fail to properly isolate the vehicle from the road. Vehicles that commonly experience suspension loads heavier than normal have heavy or hard springs with a spring rate close to the upper limit for that vehicle's weight.
This allows the vehicle to perform properly under a heavy load when control is limited by the inertia of the load. Riding in an empty truck used for carrying loads can be uncomfortable for passengers because of its high spring rate relative to the weight of the vehicle.
A race car would also be described as having heavy springs and would also be uncomfortably bumpy. A luxury car, taxi, or passenger bus would be described as having soft springs. Vehicles with worn out or damaged springs ride lower to the ground which reduces the overall amount of compression available to the suspension and increases the amount of body lean. Performance vehicles can sometimes have spring rate requirements other than vehicle weight and load.
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Spring rate is a ratio used to measure how resistant a spring is to being compressed or expanded during the spring's deflection. The magnitude of the spring force increases as deflection increases according to Hooke's Law. Briefly, this can be stated as. The negative sign indicates the direction of applied force and force exerted by spring are opposite.
Spring rate is confined to a narrow interval by the weight of the vehicle, load the vehicle will carry, and to a lesser extent by suspension geometry and performance desires. A non-linear spring rate is one for which the relation between the spring's compression and the force exerted cannot be fitted adequately to a linear model.
The spring rate of a coil spring may be calculated by a simple algebraic equation or it may be measured in a spring testing machine. The spring constant k can be calculated as follows:. Wheel rate is the effective spring rate when measured at the wheel as opposed to simply measuring the spring rate alone. Wheel rate is usually equal to or considerably less than the spring rate. Commonly, springs are mounted on control arms, swing arms or some other pivoting suspension member. Let's assume the spring moved 0.
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The wheel rate is calculated by taking the square of the ratio 0. Squaring the ratio is because the ratio has two effects on the wheel rate. The ratio applies to both the force and distance traveled. Wheel rate on independent suspension is fairly straightforward. However, special consideration must be taken with some non-independent suspension designs.
Take the case of the straight axle. When viewed from the front or rear, the wheel rate can be measured by the means above. Yet, because the wheels are not independent, when viewed from the side under acceleration or braking, the pivot point is at infinity because both wheels have moved and the spring is directly inline with the wheel contact patch.
The result is often that the effective wheel rate under cornering is different from what it is under acceleration and braking. This variation in wheel rate may be minimised by locating the spring as close to the wheel as possible. Wheel rates are usually summed and compared with the sprung mass of a vehicle to create a "ride rate" and corresponding suspension natural frequency in ride also referred to as "heave". This can be useful in creating a metric for suspension stiffness and travel requirements for a vehicle. Roll rate is analogous to a vehicle's ride rate, but for actions that include lateral accelerations, causing a vehicle's sprung mass to roll about its roll axis.
It is expressed as torque per degree of roll of the vehicle sprung mass. The roll rate of a vehicle can, and usually does, differ front to rear, which allows for the tuning ability of a vehicle for transient and steady state handling. The roll rate of a vehicle does not change the total amount of weight transfer on the vehicle, but shifts the speed and percentage of weight transferred on a particular axle to another axle through the vehicle chassis. Generally, the higher the roll rate on an axle of a vehicle, the faster and higher percentage the weight transfer on that axle.
Roll couple percentage is a simplified method of describing lateral load transfer distribution front to rear, and subsequently handling balance. It is the effective wheel rate, in roll, of each axle of the vehicle as a ratio of the vehicle's total roll rate. It is commonly adjusted through the use of anti-roll bars , but can also be changed through the use of different springs.
Weight transfer during cornering, acceleration or braking is usually calculated per individual wheel and compared with the static weights for the same wheels. The total amount of weight transfer is only affected by four factors: the distance between wheel centers wheelbase in the case of braking, or track width in the case of cornering the height of the center of gravity, the mass of the vehicle, and the amount of acceleration experienced.
The speed at which weight transfer occurs as well as through which components it transfers is complex and is determined by many factors including but not limited to roll center height, spring and damper rates, anti-roll bar stiffness and the kinematic design of the suspension links. In most conventional applications, when weight is transferred through intentionally compliant elements such as springs, dampers and anti-roll bars, the weight transfer is said to be "elastic", while the weight which is transferred through more rigid suspension links such as A-arms and toe links is said to be "geometric".
Unsprung weight transfer is calculated based on the weight of the vehicle's components that are not supported by the springs. This includes tires, wheels, brakes, spindles, half the control arm's weight and other components.
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These components are then for calculation purposes assumed to be connected to a vehicle with zero sprung weight. They are then put through the same dynamic loads. The weight transfer for cornering in the front would be equal to the total unsprung front weight times the G-Force times the front unsprung center of gravity height divided by the front track width. The same is true for the rear.
Sprung weight transfer is the weight transferred by only the weight of the vehicle resting on the springs, not the total vehicle weight. Calculating this requires knowing the vehicle's sprung weight total weight less the unsprung weight , the front and rear roll center heights and the sprung center of gravity height used to calculate the roll moment arm length. Calculating the front and rear sprung weight transfer will also require knowing the roll couple percentage.
The roll axis is the line through the front and rear roll centers that the vehicle rolls around during cornering. The distance from this axis to the sprung center of gravity height is the roll moment arm length. The total sprung weight transfer is equal to the G-force times the sprung weight times the roll moment arm length divided by the effective track width.
The front sprung weight transfer is calculated by multiplying the roll couple percentage times the total sprung weight transfer. The rear is the total minus the front transfer. Jacking forces are the sum of the vertical force components experienced by the suspension links.
The resultant force acts to lift the sprung mass if the roll center is above ground, or compress it if underground. Generally, the higher the roll center , the more jacking force is experienced. Travel is the measure of distance from the bottom of the suspension stroke such as when the vehicle is on a jack and the wheel hangs freely to the top of the suspension stroke such as when the vehicle's wheel can no longer travel in an upward direction toward the vehicle.
Bottoming or lifting a wheel can cause serious control problems or directly cause damage.
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The control problems caused by lifting a wheel are less severe if the wheel lifts when the spring reaches its unloaded shape than they are if travel is limited by contact of suspension members See Triumph TR3B. Many off-road vehicles , such as desert racers, use straps called "limiting straps" to limit the suspensions downward travel to a point within safe limits for the linkages and shock absorbers.
This is necessary, since these trucks are intended to travel over very rough terrain at high speeds, and even become airborne at times. Without something to limit the travel, the suspension bushings would take all the force when the suspension reaches "full droop", and it can even cause the coil springs to come out of their "buckets" if they are held in by compression forces only. A limiting strap is a simple strap, often nylon of a predetermined length, that stops the downward movement at a preset point before the theoretical maximum travel is reached.
The opposite of this is the "bump-stop", which protects the suspension and vehicle as well as the occupants from violent "bottoming" of the suspension, caused when an obstruction or hard landing causes the suspension to run out of upward travel without fully absorbing the energy of the stroke. Without bump-stops, a vehicle that "bottoms out" will experience a very hard shock when the suspension contacts the bottom of the frame or body, which is transferred to the occupants and every connector and weld on the vehicle. Factory vehicles often come with plain rubber "nubs" to absorb the worst of the forces, and insulate the shock.
A desert race vehicle, which must routinely absorb far higher impact forces, may be provided with pneumatic or hydro-pneumatic bump-stops. These are essentially miniature shock absorbers dampeners that are fixed to the vehicle in a location such that the suspension will contact the end of the piston when it nears the upward travel limit.
These absorb the impact far more effectively than a solid rubber bump-stop will, essential because a rubber bump-stop is considered a "last-ditch" emergency insulator for the occasional accidental bottoming of the suspension; it is entirely insufficient to absorb repeated and heavy bottomings such as a high-speed off-road vehicle encounters. Damping is the control of motion or oscillation, as seen with the use of hydraulic gates and valves in a vehicle's shock absorber. This may also vary, intentionally or unintentionally. Like spring rate, the optimal damping for comfort may be less than for control.
Damping controls the travel speed and resistance of the vehicle's suspension. An undamped car will oscillate up and down.
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With proper damping levels, the car will settle back to a normal state in a minimal amount of time. Most damping in modern vehicles can be controlled by increasing or decreasing the resistance to fluid flow in the shock absorber. See dependent and independent below. Camber changes due to wheel travel, body roll and suspension system deflection or compliance. Depending on the tire and the road surface, it may hold the road best at a slightly different angle. Small changes in camber, front and rear, can be used to tune handling. Often, too much camber will result in the decrease of braking performance due to a reduced contact patch size through excessive camber variation in the suspension geometry.
The amount of camber change in bump is determined by the instantaneous front view swing arm FVSA length of the suspension geometry, or in other words, the tendency of the tire to camber inward when compressed in bump. Roll center height is a product of suspension instant center heights and is a useful metric in analyzing weight transfer effects, body roll and front to rear roll stiffness distribution. Conventionally, roll stiffness distribution is tuned adjusting antiroll bars rather than roll center height as both tend to have a similar effect on the sprung mass , but the height of the roll center is significant when considering the amount of jacking forces experienced.
Due to the fact that the wheel and tire's motion is constrained by the suspension links on the vehicle, the motion of the wheel package in the front view will scribe an imaginary arc in space with an "instantaneous center" of rotation at any given point along its path. The instant center for any wheel package can be found by following imaginary lines drawn through the suspension links to their intersection point. A component of the tire's force vector points from the contact patch of the tire through instant center.
The larger this component is, the less suspension motion will occur.