Tuesday, April 16, 2019

What is rubber oil seal?

When we talk about the shaft in the mechanical system which most have rotation which the shaft is supported by bearings. The bearing of the shaft is mounted to the housing to support the shaft weight, in which the housing is filled with lubricants Such as lubricant At the point where the shaft is out the oil seal is installed in that position. There is a duty to protect the liquid that is used to lubricate the outer shaft. In addition, oil seals are used to leak chemicals, water and many other fluids. Many types of oil seals are also designed to be able to prevent dust or dirt from entering into the oil or lubricant.



Rubber Friction mechanism

In the design and development of rubber product such as tire , rubber seal , rubber automotive part , it is important to evaluate the contact load dependency of the friction coefficient. Mechanism of friction in rubber generates three different forms of friction: adhesion, deformation, and wear, which  adhesion force is the most influential component in rubber friction in dry conditions and low speed so that  adhesion friction is dominant for smooth contact at low speeds and dry conditions. Therefore increasing friction adhesion is possible by increasing the contact area of the product. Product samples that influence of the adhesion force is the industrial tire used in the warehouse where the floor is smooth and dry.
The hysteresis component of friction is caused by the bulk deformation of rubber material as it comes into contact with pavement asperities. Such deformation causes energy losses as rubber slides over the pavement surface. These energy losses are caused by the hysteretic.  In the case of contact between a rubber specimen and a rough hard surface , such as contact between tire and asphalt, the hysteresis component becomes dominate. 
The third major component of friction (cohesion losses) is caused by the wearing of rubber as it slides over the pavement surface. Pavement texture has an important role in the friction components—a recent study showed that higher pavement microtexture and macrotexture result in higher frictional properties. 

Sunday, April 14, 2019

About Arrhenius theory

Who was Arrhenius ?. Svant August Arrhenius was born 19 February 1859 , Vik , Sweden and died 2 October 1927 , Stockholm , Sweden . He graduate from Stockholm university , Sweden . He work about chemical kinetic and physical chemistry.

Assumption for Arrhenius theory.

  • The rate of each chemical step involved in the oxidation process(initiation , oxygen uptake,termination) must respond the same to changes in temperature.
  • The oxidation proceeds uniformity throughout the material.


Arrhenius theory is originally derived from thermodynamics. When these assumption hold, the rate of oxidative aging, at the use temperature  T1, can be determined from the aging rate measured in the lab at a least temperature T2 . Arrhenius equation can write as follow

     k = A*exp(-Ea/RT)

When
k is rate
A is Pre Exponential factor
Ea is Activation Energy
R is gas constant
T is Temperature (Kelvin)

We  can  write another format of Arrhenius equation as follow

ln(k) = -(Ea/R)*(1/T) + ln(A)

Activation Energy is the minimum energy by which the colliding molecules of sample must have in order to bring about the degradation reaction. Lower the value of activation energy, higher will be the rate at which the degradation will proceed and vice-versa.

Testing for analysis with Arrhenius is

  • Tensile , % Elongation , Modulus (ASTM D412)
  • Tear Test (ASTM D624)

Elastomers In Automotive Shaft Seals

Common elastomer  or rubber mainly used , Seals are divided into categories according to the following parts:

Engine Part                 Past used : VMQ               Current : FKM    Future  : HNBR or FKM
Transmission Part       Past used : VMQ or P.A.   Current : EAM    Future  : FKM
Pinion Part                  Past used : NBR or P.A.    Current : FKM    Future  : FKM
Wheel Part                  Past used : NBR                Current : EAM    Future  : EAM
Steering Part               Past used : NBR                Current : FKM    Future  : HNBR
Bearing Part                Past used : NBR                Current : NBR    Future  : HNBR or NBR

Seal must withstand effect of oxidized oils and oil additive , surface hardening of fluoroelastomers. For oil seal ; Seal functional mode is under static and dynamic load .

Properties of seal that must be consider

  • Dimensional stability
  • Modulus
  • Permanent Set resistance
  • Abrasion resistance , dry and/or lubricated
  • Resilience
  • Tear Strength
  • Tensile and Elongation properties
  • Excellent oil resistance
  • Good fuel resistance






Sunday, October 28, 2018

Life Prediction of O-Rings

Life prediction of O-Ring can use compression stress relaxation test because most polymeric part are intended to be in service for several year. O-Ring experience changes in properties under heat , high temperature, mechanical stress and fluids. Service life prediction of  an O-Ring is of practical and engineering interest to predict the behaviour of the component over the service life cycle. Main factor for O-Ring degradation can shown in picture 1

O-Ring

The two important properties of O-Ring are compression stress relaxation and resilience. Resilience is a measure of the ability of the seal to retract to its original shape after a constraint has been removed. The force decay of elastomer component under constant compressive strain is known as compression stress relaxation. The test measures the sealing force exerted by seal or O-Ring under compression between two plates.

Test condition for compression stress relaxation. 
  • Accelerated aging : Accelerated Oven Aging at 100 , 125 and 150 degree celsius. 
  • Sample were aged inside jigs with 25% compression.
  • Failure Criteria : Compression stress relaxation 40%
Compression stress relaxation test data is used to Service Life prediction by Arrhenius equation and WLF equation. 

Monday, May 2, 2016

What is the standard test for oil seal.

In designing oil seals what is important is the type of rubber used as material oil seals must be oil resistance properties well under working condition. Important information for user-defined testing properties of materials used to make oil seals are as follows.
1. Type of oil such as lubricant , hydrolic oil.
2. Temperatue of oil at working condition
3. Pressure of oil at working condition
4. Shaft Speed (In the case of the rotating shaft)

The standard test used to test the resistance of the oil is ASTM D471 Standard Test Method of Rubber Property-Effect of Liquids. This test method only those failures caused to determine the likehood that an oil might cause premature sealing system failures in field use.

Measure
1. volume swell (% Volume Change)
2. excessive rubber hadening
3. elongation loss
4. Stress Relaxation

Testing of the material properties of the oil seals of NOK Oil seal material found that Viton® or Fluorocarbon (FKM) is the rubber has heat resistance. It also has excellent resistance to oil and chemical. It is the best rubber for oil seals due to its well-balanced charecteristics. However, this material is not resistant types of brake fluid (DOT 3 , DOT5 glycol base) refrigerants (R32 and R134a)  Anti freeze Solution ans water stream.

Thursday, April 7, 2016

Oil Seal : An introduction

Oil seal is a component of the machinery that is used to seal lubricants or seal . Lubricants are used in the part of the machine that contact to ensure that they are moving evenly and last longer. Oil seals are used to prevent fluid from leaking through "The gap of bearings" of the machine. With the advancement of engineering thus not only necessary to prevent the leakage of the lubricant but to prevent the water chemicals or dust into the machine. Oil seal is used to serve both these respects. O-rings have a mechanism of action similar to the oil seals. Oil seal is used mainly in applications with rotating shaft.

Structural components of the oil seals consist of three parts.
   1 Elastomeric Sealing Matterial (rubber seal)
   2. Metal Case (sealing frame).
   3. Gartor Spring (Spring Press).

The materials used to produce the rubber seal. The materials used to manufacture rubber seals used in the manufacture oil seals are many different types but the most widely used in mechanical parts common to have a few species. The species that need very special will be produced and used locally, but the price will be higher as well. Popular materials are summarized as follows.

1. Nitrile (NBR)
  
Nitrile rubber is a common group of acrylonitrile terpolymer Butadiene by arylonitrile nitrile compound is a major component (18% to 50%), affecting the physical properties of the material. Impact resistance and heat the oil in a temperature range of -40 ° C to 120 ° C (oil) or 90 ° C (water) while also having the flexibility and resistance to compression force. Nitrile rubber has better mechanical properties compared to other types of rubber and a high wear resistance. It is commonly used in the oil seals.


2. EPDM (Ethylene Propylene)
   EPDM is polyethylene (ethylene) and polypropylene (propylene), which Ehylenepropylene diene- (EPDM) are produced using monomers III and is particularly useful for sealants in hydraulic fluids. Spring Cleaning The broad operating temperature range -65 ° F to 300 ° F (-55 ° C to 150 ° C) In addition, the use of steam and temperatures below the normal temperature applications as well.


3. Viton® or Fluorocarbon (FKM)
  
Viton® (fluorocarbon rubber) has many great features that have been developed to produce a rubber seal. The property unprotected in high temperature in every condition, air, fuel, hydraulic devices, fuels, solvents, or chemical solvents are some tons of material that is chosen. rubber Seal (Seal rubber) Viton® is capable of a temperature range of -15 ° F to 450 ° F (-26 ° C to 232 ° C).



Viton Oil Seals for Motor Hydrolic and gear box


Viton Oil Seals  for Motor Hydrolic and Gear box





Sunday, April 7, 2013

Tire Performance : Tread wear and vibration of tire

Wear is an indication of the life service of the tire. At each point with in the tire footprint, there is a normal contact force and a set of tanget force. When the resultant in-plane force exceeds the friction resistances associated with the normal force at a given point, the point slips and abrasion energy is generated.
We will consider the factors that affect tire wear. More even pressure distributions reduce the number of low pressure point and minimize the likelihood of slippage. High lateral forces associated with sharp cornering increase the likelihood of slipage and thus accelerate the tread wear. Tread wear is also dependent on the road texture, tread material properties and the temperature (High temperature High tread wear). Life service of tire or tread life is defined as the travel distance at which the nonskid depth reaches a specified value. Thus, all things being equal, the nonskid should be maximized to maximize tread life. For industrial tire, life service  or tread life is defined as the working time at which the nonskid depth reaches a specified value. However, too deep a nonskid can lead to unstable tread block elements, which may result in uneven wear and poor handling performance. Driver should buy the depth gauge for measure the tire wear of his tire. A key feature of tread wear performance is the evenness of wear. Uneven wear generate noise and ride disturbances and causes additional premature wear of isolated spot on the tread surface. Tire swiching inside/outside wheel position is reduce uneven wear. In industrial tire uneven wear generate radial crack on side wall.
Tire vibration charateristics of a tire design can be computed by finite element analysis(FEA), yielding the natural frequencies and associated mode shapes in the radial, lateral, and circumferential directions. The mode shapes and natural frequencies can also be measured by rolling the tire on  drums or flat tracks and measuring the tire response. To prevent resonace, the tire's  first natural frequencies should be different from the vehicle' s naural frequencies.

Sunday, March 17, 2013

Rubber to metal bonding

Rubber to metal bonding is used in wide industrial such as shaft seals, gaskets, engine mount ,rubber rolling, bridge bearings etc. Elastermer selection is important in rubber product that present above. In this content we will present principal and performance of rubber to metal bonding detail as below. 
Principal of bonding agents
  • Applied like tackfree paints or varnishes to bond elastomers on rigid substrates under vulcanization conditions.
  • Advantage , Simultaneous molding and bond formation process between elastermer and substrate.
Requirement of bonding agents
  • Bond strength such as initial bonding . type of elastomer and vulcanization system.
  • Application such as application method, film formation and drying condition.
  • Storage such as shelf lift at variable temperature, freeze-thaw-stability and heat resistance.
  • Processing such as vulcanization method, prebreaking, method fouling and short curing cycles.
  • Resistance such as boiling water, salt spray climate, glycol and heat etc.
Product of rubber to metal bonding.
There are two type as standard product and special product. Standard products has three products as primer, covercement and one coat bonding agent. Special products has two product as waterbased bonding agents and electrostatic sprayable bonding agents.
Bonding performance.
Bonding performance influence  from rubber selection , hardness of cured rubber , carbon black concentration and type of carbon black, anioxidant or antiozonants type, curative, compound cure, plasticizer concentration and type.
Adhesive selection.
  • Which elastomer stock?
  • Durometer of the cured rubber compound.?
  • Cure speed?
  • Rigid substrate selection?
  • Special pre-bake and or sweep requirements.
  • How will adhesive be applied to the metal?

Instruction of rubber to metal bonding
Figure 1 Instruction of rubber to metal bonding

How to apply rubber to metal bonding.
  • Brush coating used in small scale ; usually applied undiluted.
  • Spray coating : used in large scale ; using jig for complex and specified area shape.
  • Dip coating : used in large scale ; avoiding tears and fatty edges from dip tank.
  • Roller coating : used in large flat sheets or roller components ; low product waste , uniformity film thickness.


Figure 2 example of rubber to metal bonding*

Hysteresis effect in race car tire and street car tire.


Tires are made from rubber, which is a viscoelastic material the loading and unloading stiffness curve are not exactly the same thus which make a loop with the unloading curve below the loading. The area within the loop is the amount of dissipated energy during loading and unloading. We are called hysteresis loop or damping properties .As a tire rotates under the weight and carry load of a vehicle, it experiences repeated cycles of deformation and recovery and it dissipates energy loss as heat. The amount of dissipated energy depends on the mechanical characteristics of the tire. Hysteresis energy loss in rubber decreases as temperature increases. The hysteresis effect causes a loaded rubber not to rebound fully after load removal.
Consider a high hysteresis race car tire rolling over road irregularities. The deformation tire recovers slowly and therefore, it cannot push the footprint tail on the road as hard as the footprint head. The difference in tail and head pressure causes a resistance force, which is called rolling resistance. Race car have high hysteresis tire to increases friction and limited traction that improve stability during running match. Street car such as passenger car  truck tire and solid tire have a low hysteresis tire to reduce the rolling resistance and low operating temperature that improve fuel consumption.  Hysteresis level of tire inversely effect the stopping distance such as a high hysteresis tire make the stopping shorter however it wear rapidly and has a shorter life time but do not affect with race car .

Sunday, June 24, 2012

Rubber in Automotive

Approximately 500 - 600 application in the automobile involve the use of elastomer. These uses vary from model to model and from year to year. Automotive people are continully faced with material, design, process and cost decision in choosing elastomers to established performance goal. These goals can include durability, economy and meeting government regulation depending on the application.
Automotive standard for elastomer.
A complete rubber component standard is necessary for the following reasons
  1. To ensure selection of material that meet requirement.
  2. To prevent change in production material without the users's knowledge.
  3. To correlate design requirement  with material properties.
  4. To make certain that the material are commercially available.
  5. To maintain uniform quality in production shipments.

The requirements of a rubber component specification are as follow:
  1. Material requirement such as color , type of materials finished part quality.
  2. Performance requirement such as density, tensile , elongation and tear.
  3. Description of test methods including SAE, ASTM, and other laboratory procedure.
  4. Construction requirement for composite materialsuch as hoses head gaskets .
  5. Dimensional requirement , any information on tolerance or thickness of material referred to in the standard is required.
  6. Sampling instruction , including sample size and number of sample to be submited.
  7. Packaging instruction, to ensure clean, distortion-free part after shipment and storage.



Wednesday, May 16, 2012

Testing and quality control of foam rubber

Foam rubber is a consumer product. Therefore various national standards organizations have taken steps to ensure the production and marketing of good quality foam rubber . Important properties tested for quality control and their specification limits are given in that follow.
  • Indentation hardness index
  • It is the load in kilograms required to give an indentation  in the sample equivalent to 40% of the original thickness of the sample under specified condition. It is a measure of the load bearing capacity of the foam rubber. Foam rubber product are graded by indentation hardness such as Code A has 7-14 indentation hardness.
  • Compression set
  • It is a measure of state of cure of the foam rubber . The test consists of compressong the test piece under specified condition of time, temperature and constant deflation and noting the effect on the height of the released test sample.The compression set of the sample when determined by the first method shall not exceed 15% and by the second method shall noe exceed 5%
  • The color of latex foam rubber shall be as agreed between the purchaser and supplier.
  • Flexing test that involves submitting the whole sample to a continuous flexing with an indenter for 2,500,000 cycles at 4 Hz and measuring the loss in hardness and thickness.
  • Aging test 
  • The test sample of aging test is kept in an oven at 70 +/- 1 *C for 168 hr. Upon removal from the oven after 10 hr, the hardness is measured. The hardness of the test sample after aging shall not vary by more than +/- 20% of the value obthained with the unaged test sample.
  • Metallic Impurities
  • The copper and manganese content in the test sample shall not be more than 0.001 and 0.005% respectively.

Wednesday, March 21, 2012

How to used a waste rubber?

Regenerated rubber is often popularly known as reclaim rubber in the tires and rubber industry. This is becoming more and more popular with the increase in natural rubber and synthetic rubber prices. Regenerated rubber is a product obtained from waste and worn out vulcanized scrap. Use of reclaim rubber is already established in automotive tires, butyl tube. Energy recovery is one of the important processes of tires reclaim. Tires (once the steel wire is removed) have a relatively high specific heat value, as compare to coal. Worldwide energy recovery makes up one of the largest uses of reclaim tires. Test suggests that the use of waste tires as a substitute for coal result in lower emissions of nitrogen and sulfur. There has been a significant amount of reclaim tires used in cement kilns.

The rubber industry worldwide has focused mainly on the disposal of waste rubber rather than recapturing the economic value of the resources incorporated in the waste, historically the uses for waste rubber have been of low economic value, resulting in a low volume of recycling and stockpiling of tires. Tires are consider as the most visible of waste rubber product and their accumulation is increasing at an alarming rate worldwide.

There is an enormous potential for reclaim and reuse of rubber in developing countries. Whether rubber tires are reused, reprocessed, or used for making article for human use, the end result is there is less waste and less degradation of these materials which could cause harmful effects in our environment.

In Asian countries there has been a culture to reuse and to recycle all materials. Other than making reclaim rubber, scrap tires parts have also been used in shoe soles, slippers and in washers. Worn out tread have been nicely stripped off and used on the wheel of bull carts. Sidewalls of a tires are stripped off and knitted nicely with steel wire to make mats, mattresses and flooring products. Worn out bladders have been used in making flower garden and so on.

There is tremendous potential for the application of rubber crumb (powder rubber) in the construction of road. Crumb rubber may be used as : Fill material , In asphalt(wet and dry), As a crack sealant and in repair membranes.

Tuesday, March 20, 2012

What is rubber roll?

The application of rubber to the surface of metal cores to make rubber covered rolls generally referred to as rubber roll. The function of rubber roll in various application are diverse, demanding different properties from the rubber that is used. One of the the most extensive uses of rubber roll is in the control liquids by pressing or squeezing, as exemplified in the manufacture of paper and in the processing of metal, textiles, plastics, and leather. Such typical device as the press roll, the touch roll, the padding roll and the transfering roll.

Rubber roll are used for many conveying purposes such as feed rools and guide rools of various kinds, as used in the paper steel textile and plastic industries. The properties of rubber that are important for such application include elasticity, friction abrasion resistance and chemical resistance . In advantage resistance to solvents and plasticizer as well as resistance to heat are desired in application such as laminating, embrossing and coating.

The design of rubber roll involves considering of general factor such as the work place, the working condition, the desire performance and the required durability. The core is designed on factors such as the load, the speed and the the required precision. The core may be built the seamless, welded or cast pipe and may be made from mild steel, cast iron, stainless steel etc. It is almost possible to vulcanize soft rubber satisfactorily to the cast iron core because during vulcanization heat drives gases out the porous iron causing blisters in the covering and resulting in early service failure. To overcome this problem a layer of ebonite is applied to the core and before the soft rubber cover.

Sunday, February 5, 2012

How to design tires compound

Customers demand quality products. This will be as true in the feature as it is today. Tire are also designed to meet spectrum of service and enveronment condition. Aricraft and earthmover tires are the most advanced global tires that are specific for service, vehicle and enveronmental condition. The key properties to design tire tread compound is abrasion, heat buildup , wet grip and tear strength. Other properties that required is ease of processing. Different methods are used to develop the wide range of compounds required. Some compounds have ralatively simple application requirements, and some call for very complex properties that come close to the limits of materials and compounds. There for the same development process is not required for every compound. Some compounds are developed simply by making small changed in existing compound . Both tire technology and compound technology are changing as a result of trial and error, and intuition to become more scientific and predictive.

Sunday, November 27, 2011

Rubber properties : Freezing

The effects of temperature so far described take place instantaneously with any change of temperature. There is , however at least with certain types of rubber including natural rubber, another effect which is produced by long exposure to moderately low temperature. This is a gradual hardening, often referred to as ‘freezing’ , due to the tendency of part of neighbouring molecules to line up in parallel ; this permits stronger intermolecular attractions which bind the parallel molecule segments into a more or less rigid ‘crytallite’ , to use a familiar, though not very accurate, name. This process is quite gradual and proceeds over periods of many days; it is most rapid at a particular temperature which in the case of natural rubber about –25 *C . Vulcanisation reduces, though it does not eliminate, this technically undesirable effect, which must be noted especially in connection with the storage of rubber articles. The change from rubber-like to glass-like properties occurs at a temperature called the glass transition temperarture. Certain other properties also change suddenly at this temperature, for instance, the coefficient of thermal expansion is less below the glass transition temperature, but rubber is never used in practice below this temperature. Another inportant consequence of the influence of temperature on deformation rate is that, broadly speaking, the behaviour of rubber is change in the same way either by increasing the rate of deformation or by lowering the temperature; conversely, reducing the deformation rate produces the same effect as raising the temperature. There is, in fact, a fundamental relationship between temperature and strain-rate effect.

Monday, September 5, 2011

Cellular rubber (Foams)

There are two processes for the manufacture of foams from natural and synthetic latices. The introduction of air or gas into the latex to create foam is common to both processes. This foam is then gelled, cast into moulds, vulcanised and dried. With latex beating the latex mix is suspended in soap or gelatine and beaten from a 7- to 14-fold vulcanisable volume. For this machine wire beater with a selected steplessly variable beater speed is used. Gelling with sodium silicate fluoride keeps the foam for an extended time in a castable condition. The foam is cast into a mould and vulcanised at approximately 373 K . The cured foam rubber is removed from the mould washed free of clinging chemicals and dried.

With blown latex, hydrogen peroxide is added together with blowing agents to a vulcanisable latex mix which is decomposed. The created oxygen foams up the volume of the latex from 8 to 14 fold, the foam consisting of small regularly spaced cells. It is frozen at 258 to 263 K and carbon dioxide is passed through the rigid foam. After thawing out, the foam becomes liquid. It is then vulcanised, washed and dried in the usual way.

The manufacture of plastic foams is basically different from natural and synthetic latex foams. Polystyrene foam contains a blowing agent which expands by heating the mass to over 350 K and produces a cell structure. With polyether or polyester respectively the foam structure is built by a chemical reaction which releases carbon dioxide; the mass rises and sets simultaneously.

Sunday, September 4, 2011

Rubber properties : Endurance limit

The strength of rubber under a continuous oscillating stress is of particular significance because such an application occurs so frequently in practice. By endurance strength is meant that stress which a rubber can sustain indefinitely under an oscillating load without damage. It is experimentally ascertained with help of suitable fatigue-tensile machines through a stress-frequency curve. Modern rubber testing machines permit the rubber to be subjected to a loading which corresponds to the one occurring in practice. Thus a good insight is achieved into the elastic and thermal relationship, especially into the fatigue life.

Wednesday, August 17, 2011

Thermal properties of rubber compound : thermal diffusivity

Thermal diffusivity can be conveniently determined by observing temperature change as a function of time for sample geometrical shapes under heating condition. Alternatively of course if k r and Cp are known or separately determine. Thermal diffusivity can be calculated from its definition as thermal diffusivity = k/r*Cp. As specific heat is an additive property, it is generally convenient to calculate specific heats of rubber compound than to measure them. Specific heat of a rubber compound is given by

Cp = w1*C1 + w2*C2 + w3*C3 + …..

where w1, w2 and w3 are weight fractions of the ingredients and C1, C2 and C3 are their specific heat. In general for rubber compound above the grass transition thermal diffusivity tends to decrease slightly with increasing temperature. This is attributed to an increase of specific heat as temperature increase. However some author stated that there is no significant change in thermal diffusivity over the temperature range from room temperature up to 140 *C.

Tuesday, August 16, 2011

How to increased thermal conductivity of rubber compound.

Thermal conductivity is the basic parameter for defining heat flow in a material. Normally the thermal conductivity of rubber compound is inversely propertional to temperature but in the range of 20-90*C, the value of thermal conductivity of both gum and carbon black filled compound are slightly changed, therefore it can be assumed that the thermal conductivity of rubber is independent of temperature without any significant error. The inclusion of filler has a marked effect on thermal conductivity of the rubber compound which postulated that 10 phr of carbon black may be expected to increase the thermal conductivity by about 17% at room temperature. In the meantime we founded that thermal conductivity was an additive property depending on the volume fraction of the ingredient by an appropriate conductivity and adding these product to the thermal conductivity of gum vulcanisate. A large dependence of conductivity on loading of carbon black was reported that thermal conductivity of rubber compound increased almost linearly with black content in the range of 10-50 phr. An experimental result clearly showed that thermal conductivity increased linearly with carbon black loading and therefore the mathermatical relations between thermal conductivity and carbon black loading were introduce as

k(w) = k(0) + 0.32w

or

k(j) = k(0) + 0.4jf

where w is the weight fraction and j is the volume fraction of crabon black.

Apart from carbon black loading carbon black structure seems to have an influence on the thermal conductivity of rubber as well. Effect of carbon black structure on thermal conductivity of NR compound we found that higher carbon black structure gives higher value of thermal conductivity. However the degree of change in thermal conductivity as a function of carbon black structure is small and is not straight forward.