# Designing TPV tubes, ducts and bellows.

This is the fourth of a series of articles that cover the general
guidelines and theory behind the design of thermoplastic vulcanizates
(TPVs). Straddling the divide between plastic part design and rubber
part design, each section covers an individual topic and can generally
stand on its own as a source of information for guiding the development
of TPV part design.

This information presents general guidelines, but each application is unique and may not conform to the guidelines set forth in this document. Some engineering judgement is required to determine the appropriate use of these guidelines.

The objective is to estimate the minimum wall thickness of a smooth wall tube to resist external/negative (vacuum) or internal/positive pressure. There are two types of applications where the design guidelines can be applied, e.g., ducts and tubes (the latter being single component without reinforcement).

These guidelines are not relevant to hoses (consisting of a lining, reinforcement and usually an outer cover), as their mechanical properties are mainly driven by the reinforcement.

Ducts

Examples include automotive clean air ducts (vacuum or external pressure), turbo air ducts (internal pressure) and appliance bellows. In such applications, a smooth wall section may be required when the space available for part envelope is limited or when longitudinally rigid sections are needed.

To avoid axial elongation, the trend in turbo air duct de sign is to maximize the proportion of smooth wall section on convoluted sections that are often made of Santoprene TPV 203-50. Considering that this trend may stiffen the air duct too much and make the clamping forces too weak to maintain the part in place, a compromise must be found between pressure resistance and flexibility. To permit the determination of that compromise, the specifications must mention the maximum reaction forces that air duct extremities should not exceed. Moreover, sequential blow molding can be used in order to combine hard and soft materials, the latter being used in the clamping/sealing area.

An oval cross-section (instead of circular) can be used if the envelope is smaller in one direction, but weakness from the greater radius must be taken into account. For a conservative calculation, the oval duct will be seen as a cylindrical duct with a radius equal to the greater radius of ellipsis. However, it is recommended to avoid as much as possible the use of oval sections, as they are not appropriate for sealing. Moreover, their processing is generally more difficult than that of a circular section.

Hydraulic tube design

While for ducts the most important parameters to consider are the absolute displacements (internal pressure) and/or the collapse pressure (external pressure), the most important parameters to determine when considering the design of tubes is the maximum working pressure (MWP), determined from the minimum burst pressure (MBP).

The MWP is a fraction of the MBP, depending on the security factor. The security factor depends on the application, but can be as high as four.

The MWP depends on the material, the geometry, the operational conditions (static, dynamic), the required working life, the required minimum bending radius, the temperature, the resistance to the media with which the tube comes into contact and/or external influences (ozone, UV light, weathering, etc.).

The theory described below concentrates on providing a formula to determine the MBP for tubes.

Material selection

The material selection is subject to the type of application and the type of process used to produce the part. Table 1 is a summary of possible materials convenient for the two applications and processes considered in this section.

Theory

The ways to estimate the resistance to external pressure, the deformation under internal pressure and the burst pressure are reviewed below. The results are only fully reliable when the deformation occurs within a strain range where linearity is found in the stress-strain relationship of the material of choice.

Depending on the type of test (tension, compression or shear), the temperature and the load speed, Santoprene TPV grades can be divided into two categories, including: the "rubber-like" material type (exhibiting a curve with a positive slope until rupture) and the "yield" material type (exhibiting a yield point and a negative slope). Most of Santoprene TPV grades are rubber-like, with the exception of 103-40 and 103-50.

The yield point at 23[degrees]C (73[degrees]F) is found to be about:

* 25% with Santoprene TPV 103-50; and

* 30% with Santoprene TPV 103-40.

It is not advised to stretch these materials over their yield point in the stress-strain relationship. Therefore, in the case of a duct application, it is important to verify that the pressure is not going above the yield point.

In the case of tubes, it is more important to determine the pressure leading to rupture (burst), rather than the pressure at the yield point. Indeed, at 23[degrees]C (73[degrees]F), the quotient between the stress at yield point and the stress at rupture is 1.5 for 103-50 and 2.25 for 103-40, while the relationship proposed to estimate the burst pressure is very conservative and significantly over this ratio for these grades (see below). Moreover, the MWP is usually referred as 1/3 to 1/4 of the MBP.

The negative pressure case

In case of a significant deviation from linearity, a non-linear FEA approach is advised to obtain an accurate answer.

With hard Santoprene TPV grades like 101-87, 103-40 and 103-50, a linear relationship is observed between 0 and 2% elongation at 23[degrees]C (73[degrees]F), and the elastic modulus (E) can be estimated, as shown below.

For all calculations, it is recommended to use 80% of the E.

[E.sub.w] = 0.8*E

Let us consider the tube in figure 1. Let us estimate, using one such method, the minimum thickness needed for a tube to resist to vacuum.

This method uses a set of design equations to determine the wall thickness of any given length of tube.

t = [r.sub.0] 1/4C [1+ [square root of 32C -4]/tan([2tan.sup.-1] [cube root of tan(A)])

where:

[r.sub.0] = external radius;

[FIGURE 1 OMITTED]

[E.sub.w] = modulus of elasticity = 0.8E;

v = Poisson's ratio = 0.47 for Santoprene TPV;

P = external pressure (internal vacuum);

A = 1/2 [tan.sup.-1] [square root of [(8C - 1).sup.3]/ [(12 - 1 - [32C.sup.2]).sup.2]

C =[E.sub.w]/{4(l-[v.sup.2])P}+1/8.

(Note: [E.sub.w] and P must have the same units).

Tips for designing smooth section

Check the specifications. A smooth section might resist a positive or a negative pressure. Typical examples are:

* A conventional automotive clean air duct should not collapse under vacuum at the highest temperature of the performance.

* An automotive turbo air duct should not extend nor blow over specified limits under a positive pressure at the peak temperature of the application.

* A hose should not rupture under specified conditions of pressure and temperature.

For a conventional automotive clean air duct, it is relatively easy to estimate the minimum wall thickness of a smooth section from the method detailed above. Remember that a reduction of volume can be obtained through the use of stiffeners, as detailed above.

With a turbo air duct, the smooth section is generally made of polypropylene or Santoprene TPV grade 103-50 to meet the requirements on stiffness at high temperatures. The wall thickness with Santoprene TPV 103-50 can be estimated from the relationship given in the relevant section above.

With a tube, the burst pressure, and here from the operating pressure, can be estimated from a simple relationship as shown above, from the knowledge of the properties at break of Santoprene TPV grades at the highest temperature of an application. Always remember that chemical resistance, resistance to kinking and resistance to abrasion might be additional driving forces in the choice of the grade.

Designing convolutes

Santoprene brand TPVs are used in a wide variety of bellow shaped parts/applications, and replace conventional thermoset rubber. The design of a thermoset rubber part typically uses thick walls to achieve strength and flexibility. TPVs can use thinner wall designs with a convoluted bellow shape with stiffer TPV grades to accomplish the same mechanical requirements. Because these TPV grades are much stiffer, the designs required are quite different from a conventional thermoset rubber. These bellow shapes are used in a wide variety of applications across a number of industries. These would include:

* Automotive clean air ducts (vacuum);

* automotive turbo air ducts (pressure);

* automotive shock absorber bellows;

* automotive rack and pinion bellows;

* automotive tie rod end seal;

* automotive constant velocity joint boot;

* automotive drive shaft boot/gear boot;

[FIGURE 2 OMITTED]

* automotive door bellow; and

* appliance bellow.

The bellows are fabricated using extrusion blow molding, injection blow and press blow molding, and injection molding. Design considerations are required to accommodate limitations for each of these processes.

Guidelines

The shape of a convolute can be described, as shown in figure 2. The terms shown here are:

where:

h = convolute height;

w = convolute pitch;

O.D. = outer diameter of convolute;

I.D. = inner diameter of convolute;

[t.sub.tip] = thickness of tip;

[t.sub.root] = thickness of root;

[r.sub.tip] = radius of tip (measured to outer surface);

[r.sub.root] - radius of root (also measured to outer surface);

theta = included convolute angle;

alpha = wall angle;

L = length of convoluted section; and

N = number of convolutes (typically counting tips).

A key relationship for convoluted bellows is based on these geometric factors:

Wall length, l, defined from the wall angle and diameters:

l = {O.D. - I.D. - [([t.sub.tip] + [t.sub.root]/2]} / sin (alpha)

Since the root thickness is usually greater, the minimum compressed length, [L.sub.min] compressed, of a convolute section is:

[L.sub.min compressed] = [r.sub.root]

For many applications, e.g., air ducts, there is a maximum

working length to which a bellow should be stretched open. This is generally described as the length at which the included angle, theta, between the convolutes reaches 90[degrees]. The equation for this length with uniform convolutes is:

[L.sub.max working] = 2 N / sin (90[degrees]/2) = 1.414 N l

Vacuum collapse resistance and pressure resistance are treated separately in other sections. Refer to these to determine how to calculate the required wall thickness and angles for applications like air ducts that are exposed to these conditions.

Geometry effects

General design of convolute shapes is dictated by the requirements for flexibility, bellows stiffness, diameters, extension and collapse limits. Some typical designs are used in specific applications. These will be discussed in separate sections following, but in general there are some guidelines that can be followed that will help to tune a design to the performance requirements of a given bellows.

In table 2, the general effect of varying the convolute design parameters will give a designer an understanding of the range of variables to adjust to achieve the balance of performance desired in a convoluted bellows for a wide variety of applications.

Convolute tip thickness should be the only thickness specified on blow molded bellows. The blow ratio will eliminate the ability to set the root thickness. The tip thickness should only be set at a minimum value for blow molded bellows since the fabricator will require some tolerance variation. The tip thickness will have the effects shown in table 3.

For processing details, please read ExxonMobil's "Guide for extrusion blow molding for thermoplastic rubbers and thermoplastic elastomers."

by ExxonMobil Chemical

(www.santoprene.com)

This information presents general guidelines, but each application is unique and may not conform to the guidelines set forth in this document. Some engineering judgement is required to determine the appropriate use of these guidelines.

The objective is to estimate the minimum wall thickness of a smooth wall tube to resist external/negative (vacuum) or internal/positive pressure. There are two types of applications where the design guidelines can be applied, e.g., ducts and tubes (the latter being single component without reinforcement).

These guidelines are not relevant to hoses (consisting of a lining, reinforcement and usually an outer cover), as their mechanical properties are mainly driven by the reinforcement.

Ducts

Examples include automotive clean air ducts (vacuum or external pressure), turbo air ducts (internal pressure) and appliance bellows. In such applications, a smooth wall section may be required when the space available for part envelope is limited or when longitudinally rigid sections are needed.

To avoid axial elongation, the trend in turbo air duct de sign is to maximize the proportion of smooth wall section on convoluted sections that are often made of Santoprene TPV 203-50. Considering that this trend may stiffen the air duct too much and make the clamping forces too weak to maintain the part in place, a compromise must be found between pressure resistance and flexibility. To permit the determination of that compromise, the specifications must mention the maximum reaction forces that air duct extremities should not exceed. Moreover, sequential blow molding can be used in order to combine hard and soft materials, the latter being used in the clamping/sealing area.

An oval cross-section (instead of circular) can be used if the envelope is smaller in one direction, but weakness from the greater radius must be taken into account. For a conservative calculation, the oval duct will be seen as a cylindrical duct with a radius equal to the greater radius of ellipsis. However, it is recommended to avoid as much as possible the use of oval sections, as they are not appropriate for sealing. Moreover, their processing is generally more difficult than that of a circular section.

Hydraulic tube design

While for ducts the most important parameters to consider are the absolute displacements (internal pressure) and/or the collapse pressure (external pressure), the most important parameters to determine when considering the design of tubes is the maximum working pressure (MWP), determined from the minimum burst pressure (MBP).

The MWP is a fraction of the MBP, depending on the security factor. The security factor depends on the application, but can be as high as four.

The MWP depends on the material, the geometry, the operational conditions (static, dynamic), the required working life, the required minimum bending radius, the temperature, the resistance to the media with which the tube comes into contact and/or external influences (ozone, UV light, weathering, etc.).

The theory described below concentrates on providing a formula to determine the MBP for tubes.

Material selection

The material selection is subject to the type of application and the type of process used to produce the part. Table 1 is a summary of possible materials convenient for the two applications and processes considered in this section.

Theory

The ways to estimate the resistance to external pressure, the deformation under internal pressure and the burst pressure are reviewed below. The results are only fully reliable when the deformation occurs within a strain range where linearity is found in the stress-strain relationship of the material of choice.

Depending on the type of test (tension, compression or shear), the temperature and the load speed, Santoprene TPV grades can be divided into two categories, including: the "rubber-like" material type (exhibiting a curve with a positive slope until rupture) and the "yield" material type (exhibiting a yield point and a negative slope). Most of Santoprene TPV grades are rubber-like, with the exception of 103-40 and 103-50.

The yield point at 23[degrees]C (73[degrees]F) is found to be about:

* 25% with Santoprene TPV 103-50; and

* 30% with Santoprene TPV 103-40.

It is not advised to stretch these materials over their yield point in the stress-strain relationship. Therefore, in the case of a duct application, it is important to verify that the pressure is not going above the yield point.

In the case of tubes, it is more important to determine the pressure leading to rupture (burst), rather than the pressure at the yield point. Indeed, at 23[degrees]C (73[degrees]F), the quotient between the stress at yield point and the stress at rupture is 1.5 for 103-50 and 2.25 for 103-40, while the relationship proposed to estimate the burst pressure is very conservative and significantly over this ratio for these grades (see below). Moreover, the MWP is usually referred as 1/3 to 1/4 of the MBP.

The negative pressure case

In case of a significant deviation from linearity, a non-linear FEA approach is advised to obtain an accurate answer.

With hard Santoprene TPV grades like 101-87, 103-40 and 103-50, a linear relationship is observed between 0 and 2% elongation at 23[degrees]C (73[degrees]F), and the elastic modulus (E) can be estimated, as shown below.

For all calculations, it is recommended to use 80% of the E.

[E.sub.w] = 0.8*E

Let us consider the tube in figure 1. Let us estimate, using one such method, the minimum thickness needed for a tube to resist to vacuum.

This method uses a set of design equations to determine the wall thickness of any given length of tube.

t = [r.sub.0] 1/4C [1+ [square root of 32C -4]/tan([2tan.sup.-1] [cube root of tan(A)])

where:

[r.sub.0] = external radius;

[FIGURE 1 OMITTED]

[E.sub.w] = modulus of elasticity = 0.8E;

v = Poisson's ratio = 0.47 for Santoprene TPV;

P = external pressure (internal vacuum);

A = 1/2 [tan.sup.-1] [square root of [(8C - 1).sup.3]/ [(12 - 1 - [32C.sup.2]).sup.2]

C =[E.sub.w]/{4(l-[v.sup.2])P}+1/8.

(Note: [E.sub.w] and P must have the same units).

Tips for designing smooth section

Check the specifications. A smooth section might resist a positive or a negative pressure. Typical examples are:

* A conventional automotive clean air duct should not collapse under vacuum at the highest temperature of the performance.

* An automotive turbo air duct should not extend nor blow over specified limits under a positive pressure at the peak temperature of the application.

* A hose should not rupture under specified conditions of pressure and temperature.

For a conventional automotive clean air duct, it is relatively easy to estimate the minimum wall thickness of a smooth section from the method detailed above. Remember that a reduction of volume can be obtained through the use of stiffeners, as detailed above.

With a turbo air duct, the smooth section is generally made of polypropylene or Santoprene TPV grade 103-50 to meet the requirements on stiffness at high temperatures. The wall thickness with Santoprene TPV 103-50 can be estimated from the relationship given in the relevant section above.

With a tube, the burst pressure, and here from the operating pressure, can be estimated from a simple relationship as shown above, from the knowledge of the properties at break of Santoprene TPV grades at the highest temperature of an application. Always remember that chemical resistance, resistance to kinking and resistance to abrasion might be additional driving forces in the choice of the grade.

Designing convolutes

Santoprene brand TPVs are used in a wide variety of bellow shaped parts/applications, and replace conventional thermoset rubber. The design of a thermoset rubber part typically uses thick walls to achieve strength and flexibility. TPVs can use thinner wall designs with a convoluted bellow shape with stiffer TPV grades to accomplish the same mechanical requirements. Because these TPV grades are much stiffer, the designs required are quite different from a conventional thermoset rubber. These bellow shapes are used in a wide variety of applications across a number of industries. These would include:

* Automotive clean air ducts (vacuum);

* automotive turbo air ducts (pressure);

* automotive shock absorber bellows;

* automotive rack and pinion bellows;

* automotive tie rod end seal;

* automotive constant velocity joint boot;

* automotive drive shaft boot/gear boot;

[FIGURE 2 OMITTED]

* automotive door bellow; and

* appliance bellow.

The bellows are fabricated using extrusion blow molding, injection blow and press blow molding, and injection molding. Design considerations are required to accommodate limitations for each of these processes.

Guidelines

The shape of a convolute can be described, as shown in figure 2. The terms shown here are:

where:

h = convolute height;

w = convolute pitch;

O.D. = outer diameter of convolute;

I.D. = inner diameter of convolute;

[t.sub.tip] = thickness of tip;

[t.sub.root] = thickness of root;

[r.sub.tip] = radius of tip (measured to outer surface);

[r.sub.root] - radius of root (also measured to outer surface);

theta = included convolute angle;

alpha = wall angle;

L = length of convoluted section; and

N = number of convolutes (typically counting tips).

A key relationship for convoluted bellows is based on these geometric factors:

Wall length, l, defined from the wall angle and diameters:

l = {O.D. - I.D. - [([t.sub.tip] + [t.sub.root]/2]} / sin (alpha)

Since the root thickness is usually greater, the minimum compressed length, [L.sub.min] compressed, of a convolute section is:

[L.sub.min compressed] = [r.sub.root]

For many applications, e.g., air ducts, there is a maximum

working length to which a bellow should be stretched open. This is generally described as the length at which the included angle, theta, between the convolutes reaches 90[degrees]. The equation for this length with uniform convolutes is:

[L.sub.max working] = 2 N / sin (90[degrees]/2) = 1.414 N l

Vacuum collapse resistance and pressure resistance are treated separately in other sections. Refer to these to determine how to calculate the required wall thickness and angles for applications like air ducts that are exposed to these conditions.

Geometry effects

General design of convolute shapes is dictated by the requirements for flexibility, bellows stiffness, diameters, extension and collapse limits. Some typical designs are used in specific applications. These will be discussed in separate sections following, but in general there are some guidelines that can be followed that will help to tune a design to the performance requirements of a given bellows.

In table 2, the general effect of varying the convolute design parameters will give a designer an understanding of the range of variables to adjust to achieve the balance of performance desired in a convoluted bellows for a wide variety of applications.

Convolute tip thickness should be the only thickness specified on blow molded bellows. The blow ratio will eliminate the ability to set the root thickness. The tip thickness should only be set at a minimum value for blow molded bellows since the fabricator will require some tolerance variation. The tip thickness will have the effects shown in table 3.

For processing details, please read ExxonMobil's "Guide for extrusion blow molding for thermoplastic rubbers and thermoplastic elastomers."

by ExxonMobil Chemical

(www.santoprene.com)

Table 1--material selection for each application type and available process External pressure Internal pressure Mono-extrusion Santoprene TPV 101-87 Santoprene TPV 101-80 is viewed as a compromise for tubes and 103-40 or between the resistance 103-50 for ducts. to collapse and sealing requirements. Choice is The grade choice may also driven by specifications be driven by fluid and economics. resistance at a high temperature. Increased wall thickness When resistance to on smooth wall sections abrasion is required, and/or use of stiffeners Santoprene 8000 TPV may may be required. be selected for tubes (or as the external layer of a hose). Co-extrusion Soft Santoprene TPV Santoprene TPV 103-40 grade for sealing at for sealing at ends and ends. Hard Santoprene a harder material for TPV grade for smooth smooth sections and convolute sections. (polypropylene or 103-50) Table 2--convolute variations Variation Variable Effect Convolute height Taller --More flexibility. (h) --Lower force to collapse and extend. --Crush resistance increase. Shorter --Less flexibility --Higher force to collapse and extend. --Crush resistance decreases. Convolute width Wider --Easier to extend. (w) --Harder to collapse. --Crush resistance decreased. Narrower --Easier to collapse. --Harder to extend. --Crush resistance increased. Convolute angle Larger --Easier to extend. Variation (alpha) --Harder to collapse. --Crush resistance decreased. Smaller --Easier to collapse. --Harder to extend. --Crush resistance increased. Convolute tip Larger --Easier to extend. Radius ([r.sub.tips]) --Harder to collapse. --Increases length of bellows. Smaller --Easier to collapse. --Harder to extend. --Decreases length of bellows. Convolute root Larger --Easier to extend. Radius ([r.sub.root]) --Harder to collapse. --Helps keep material at the root during blow molding. Smaller --Easier to collapse. --Harder to extend. --Helps distribute material to bellows tip during blow molding. Table 3 Thicker tip Thinner Up Harder to extend and collapse. Easier to extend and collapse. More resistant to abrasion Crush resistance decreased. and impact. Crush resistance increased. Square top width decreased Square top width increased Minimum collapse length Crush resistance increased. increased. Bellow length increased when Functions more like a number of convolutes same. round top.

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Title Annotation: | Tech Service |
---|---|

Publication: | Rubber World |

Date: | Apr 1, 2008 |

Words: | 2259 |

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