vvtie

VVT-iE (Variable Valve Timing - intelligent by Electric motor) is a version of Dual VVT-i that uses an electrically operated actuator to adjust and maintain intake camshaft timing.[2] The exhaust camshaft timing is still controlled using a hydraulic actuator. This form of variable valve timing technology was developed initially for Lexus vehicles. This system was first introduced on the 2007MY Lexus LS 460 as 1UR engine.

dual vvti

The Dual VVT-i system adjusts timing on both intake and exhaust camshafts. It was first introduced in 1998 on the RS200 Altezza's 3S-GE engine.

Dual VVT-i is also found in Toyota's new generation V6 engine, the 3.5-liter 2GR-FE first appearing on the 2005 Avalon. This engine can now be found on numerous Toyota and Lexus models. By adjusting the valve timing, engine start and stop occurs almost unnoticeably at minimum compression. Fast heating of the catalytic converter to its light-off temperature is possible, thereby reducing hydrocarbon emissions considerably.

Most Toyota engines including the LR engines (V10, used in the Lexus LFA), UR engines (V8), GR engines (V6), AR engines (Large I4), and ZR engines (Small I4) now use this technology.

vvtli

VVTL-i (Variable Valve Timing and Lift intelligent system) is an enhanced version of VVT-i that can alter valve lift (and duration) as well as valve timing. In the case of the 16 valve 2ZZ-GE, the engine head resembles a typical DOHC design, featuring separate cams for intake and exhaust and featuring two intake and two exhaust valves (four total) per cylinder. Unlike a conventional design, each camshaft has two lobes per cylinder, one optimized for lower rpm operation and one optimized for high rpm operation, with higher lift and longer duration. Each valve pair is controlled by one rocker arm, which is operated by the camshaft. Each rocker arm has a slipper follower mounted to the rocker arm with a spring, allowing the slipper follower to freely move up and down with the high lobe without affecting the rocker arm. When the engine is operating below 6000-7000 rpm (dependent on year, car, and ECU installed), the lower lobe is operating the rocker arm and thus the valves, and the slipper-follower is freewheeling next to the rocker arm. When the engine is operating above the lift engagement point, the ECU activates an oil pressure switch which pushes a sliding pin under the slipper follower on each rocker arm. The rocker arm is now locked into slipper-follower's movements and thus follows the movement of the high rpm cam lobe, and will operate with the high rpm cam profile until the pin is disengaged by the ECU. The lift system is similar in principle to Honda VTEC operation.
The system was first used in 2000 Toyota Celica with 2ZZ-GE. Toyota has now ceased production of its VVTL-i engines for most markets, because the engine does not meet Euro IV specifications for emissions. As a result, this engine has been discontinued on some Toyota models, including that of the Corolla T-Sport (Europe), Corolla Sportivo (Australia), Celica, Corolla XRS, Toyota Matrix XRS, and the Pontiac Vibe GT, all of which had the 2ZZ-GE engine fitted. The Lotus Elise continues to offer the 2ZZ-GE and the 1ZZ-FE engine, while the Exige offers the engine with a supercharger. The Toyota Yaris uses VVT-i on its gasoline engines.

vvti

VVT-i, or Variable Valve Timing with intelligence, is an automobile variable valve timing technology developed by Toyota. The Toyota VVT-i system replaces the Toyota VVT offered starting in 1991 on the 5-valve per cylinder 4A-GE engine. The VVT system is a 2-stage hydraulically controlled cam phasing system.

VVT-i, introduced in 1996, varies the timing of the intake valves by adjusting the relationship between the camshaft drive (belt, scissor-gear or chain) and intake camshaft. Engine oil pressure is applied to an actuator to adjust the camshaft position. Adjustments in the overlap time between the exhaust valve closing and intake valve opening result in improved engine efficiency.

In the real world, very few things have absolute, fixed probabilities. Many of the aspects of the world that we are familiar with are not truly random. Take for instance, the probability of developing schizophrenia. Say that the prevalence of schizophrenia in a population is 1%. If we know nothing else about an individual, we would say that the probability of this individual developing schizophrenia is 0.01. In mathematical notation,

                   P(Sz) = 0.01

We know from empirical research, however, that certain people are more likely to develop schizophrenia than others. For example, having a schizophrenic first-degree relative greatly increases the risk of becoming schizophrenic. The probability above is essentially an average probability, taken across all individuals both with and without schizophrenic first-degree relatives.

The notion of conditional probability allows us to incorporate other potentially important variables, such as the presence of familial schizophrenia, into statements about the probability of an individual developing schizophrenia. Mathematically, we write

                   P( X | Y) 

meaning the probability of X conditional on Y or given Y. In our example, we could write

    P (Sz | first degree relative has Sz)

and

    P (Sz | first degree relative does not have Sz)

Whether or not these two values differ is an indication of the influence of familial schizophrenia upon an individual's chances of developing schizophrenia.

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Previously, we mentioned that all probability statements depend on some kind of model in some way. The probability of an outcome will be conditional upon the parameter values of this model. In the case of the coin toss,

     P (H | p=0.5)

where H is the event of obtaining a head and p is the model parameter, set at 0.5.

Let's think a little more carefully about what the full model would be for tossing a coin, if p is the parameter. What do we know about coin tossing?

• The outcome is a discrete, binary outcome for each toss - it is either heads or tails.
• We assume that the probability of either outcome does not change over time.
• We assume that the outcome of each toss of a coin can be regarded as independent from all other outcomes. That is, getting five heads in a row does not make it any more likely to get a tail on the next trial.
• In the case of a 'fair' coin, we assume a 50:50 chance getting either heads or tails - that is, p=0.5.

Say we toss a coin a number of times and record the number of times it lands on heads. The probability distribution that describes just this kind of scenario is called the binomial probability distribution. It is written as follows :

Let's take a moment to work through this. The notation is as follows:-

• n = total number of coin tosses
• h = number of heads obtained
• p = probability of obtaining a head on any one toss

(The ! symbol means factorial (5! = 1x2x3x4x5 = 120).)

We can think of this equation in two parts. The second part involves the joint probability of obtaining h heads (and therefore n-h tails) if a coin is tossed ntimes and has probability p of landing heads on any one toss (and therefore probability 1-p of landing tails). Because we have assumed that each of the ntrails is independent and with constant probability the joint probability of obtaining h heads and n-h tails is simply the product of all the individual probabilities. Imagine we obtained 4 heads and 5 tails in 9 coin tosses. Then

is simply convenient notation for

The first half of the binomial distribution function is concerned with the fact that there is more than 1 way to get, say, 4 heads and 5 tails if a coin is tossed 9 times. We might observe

   H, T, H, H, T, T, H, T, T.

or

 

   T, H, H, T, H, T, T, H, T.

or even

 

   H, H, H, H, T, T, T, T, T.

Every one of the permutations is assumed to have equal probability of occurring - the coefficient

represents the total number of permutations that would give 4 heads and 5 tails.

So, the probability of obtaining 4 heads and 5 tails for a fair coin is

When we speak about the probability of observing events such as the outcome of a toss of a coin, we are implicitly assuming some kind of model, even in this simple case. In the case of a coin, the model would state that there is some certain, fixed probability for the particular outcomes. This model would have one parameter, p the probability of the coin landing on heads. If the coin is fair, then p=0.5. We can then speak about the probability of observing an event, given specific parameter values for the model. In this simple case, if p =0.5, then the probability of the coin landing heads on any one toss is also 0.5.

In the case of this simple example, it does not seem that we have gained very much - we seem to be merely calling what was previously a simple probability the parameter of a model. As we shall see, however, this way of thinking provides a very useful framework for expressing more complex problems.