Your 3306 was designed to use an oil that meets API oil categories, CC, CD, CD-II, and CF.
These are known as "detergent" oils and contain multiple additives to assist with the oils lubricating performance.
These oil categories have been in use since around 1960, but are now classed as "obsolete" because the newer categories produced since category CF, have replaced them.
All newer and current API oil categories are "backwards compatible" with older oil categories.
Synthetic oils have become popular in recent years because of their superior performance under harsher operating conditions.
The major difference between synthetic lube oils and regular lube oils is that the base oil for regular lube oils is refined by distillation from individual batches of crude oil - while synthetic oils are produced via "catalytic cracking", whereby a catalyst is used to create a cleaner and more desirable base oil.
Individual crudes differ greatly in the level of undesirable chemical ingredients and steps must be taken in refining to reduce, refine out, or chemically alter the undesirable ingredients in the crude that affect the performance of the final product.
Crude oils are blended from various sources and countries to try and reduce the impact of the undesirable chemicals in the raw crude.
As a result, there is always some level of undesirable chemicals in the base oil produced from straight refining - whereas the base oil from catalytic cracking is purer and has virtually no undesirable chemicals in it.
This base oil, used to produce synthetic lube oils, is essentially "tailored" in its production to achieve a highly desirable level of hydrocarbons that makes a superior-performing oil.
Base oils, regardless of their origin, are then modified again with at least 7 additives. The main additives are:
Anti-oxidants
Rust and Corrosion Inhibitors.
Viscosity Index Improvers.
Anti-wear (AW) Agents.
Extreme Pressure (EP) Additives.
Detergents.
Dispersants.
Anti-foaming Agents.
Straight grade oils are very basic oils, and can't cope with big variations in temperature.
Multi-grade oils have "viscosity improvers" added so the oil can keep a steady viscosity over a wider temperature range.
Viscosity improvers added to oil are long-chain polymers that have the curious property of becoming more viscous when cold, and thickening up when hot.
This is the opposite of oils properties, so the VI's enable the oil to stay thicker when it's hot, and to help stop it getting really thick, when it's cold.
Synthetic oils are "high performance" oils and they are designed to cope with a much wider range of harsh operating conditions than regular refined oils.
They also have higher levels of additives, and in particular, potent detergents, designed to keep high performance engines operating under heavy loads and harsh conditions, clean.
Since the advent of low-emission engines, piston and ring design has altered to allow more pollutants to go down past the rings and into the oil - rather than out the exhaust into the atmosphere.
This results in lube oils designed for use in low-emission engines needing a lot more additives and higher levels of detergents, to cope with the additional pollutant load.
The important part to keep in mind when selecting an oil for an older engine is whether the oil has a high level of detergents and other additives that will strip out beneficial carbon buildup in the older engine - and damage older seals that are often hardened and less flexible.
Beneficial carbon deposits assist in ring sealing and in oil seal sealing in older engines - so if you strip these out with a current variety of high performance lube oil, you will start to see increased oil consumption, increased blowby and more oil leaks.
Finally, the synthetic oils cost more because catalytic cracking is an expensive process, as compared to straight refining.
My choice would be to use a multi-grade oil, such as 15W-40, which covers a good temperature range for your region, and to select an API grade that is CH-4 or older (some manufacturers still produce CD, CE and CF grade oils) - and keep away from synthetic oils that are unnecessarily expensive for your older tractor.
It would be advisable to try and find out what oil category was previously used in your tractor, so you don't replace it with a more potent one, that is going to essentially "clean out" the inside of your engine, and cause problems.
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