High-pressure measurement technology continues to develop steadily and so does the **design of high-pressure transducers** from HBM. What makes these transducers so special? High-pressure transducers from HBM are equipped with a **monolithically structured measuring body** in which the electro-mechanical conversion of the signal is implemented by means of a **foil strain gauge***. This design has proven itself over the years and has furthermore developed to become the **standard in high-pressure measurement technology**. The monolithic structure of the measuring body has excellent measuring properties, exhibiting extraordinary** accuracy, robustness and stability**.

Process pressures used in high pressure applications are raised to higher levels to increase the **cost-effectiveness of processes**. For example, a **higher pressure** **in water jet cutting **makes it possible to achieve **higher cutting thicknesses **and increase **cutting speed **dramatically. Currently the pressure level for this technology is between **4000 and 6000 bar**. The continually rising requirements for **maximum pressure, overload stability and especially accuracy** accompanying this trend have led to sustained and consistent **development in high pressure measurement technology**.

## 1. Principle of measurement

The strain gauges are applied to **metallic spring elements** on the pressure transducers. The spring element is mechanically** deformed **by the pressure in the elastic range only (straight line by Hooke's law).

In foil strain gauges the measuring grid length l is related to the measured change in length *ΔL*. This means that **an SG integrates stress over the length of the measuring grid**. To generate the **highest possible electrical output signal**, the SG is applied in the area of the **greatest positive and negative strain or stress** (*see Fig. 1*).

*Fig. 1: Integration of the strain gradient*

**Knowing the exact strain gradient and distribution** makes it possible to adapt the shape, position and length of the SG measuring grid optimally to the **geometry of the measuring body**. Because the SG is applied in the last step, the measuring body can thus be optimized for **all the demands of high pressure applications**. There are **no design limitations in terms of the measuring body design**. The optimized geometry of the measuring body also makes it possible to distribute strain so that only **very slight strain gradients** are exhibited – a real plus in terms of **robustness and resistance** to alternating loads.

If the resistance of individual SGs changes slightly due to pressure loading, a clearly measurable **output voltage** is generated as a result. **Output signals** of different magnitudes are generated depending on the measuring range. This is also referred to as sensitivity. Connecting the SGs to a **Wheatstone bridge **makes it possible to add the strain values. A typical nominal (rated) sensitivity for pressure transducers up to 2500 bar with foil strain gauge technology is 2 mV/V.

**Measuring bodies and strain gauges** represent the two essential elements for **converting pressure into an electrical signal**. The spring element is deformed by the pressure that is applied. A strain gauge then records the resulting surface strain. Finally the Wheatstone bridge converts the change in resistance of the SG into a proportional change in voltage, which is then further processed in a downstream measuring amplifier (*see Fig. 2*).

*Fig. 2: Basic layout of a measuring chain*

## 2. Monolithic measuring body design

### 2.1 Effect on service life and endurance fatigue

In addition to accuracy, **service life** plays an especially important role in dynamic loading and therefore in the design of the measuring body in high-pressure measurement technology.

For steels commonly used to construct transducers, the **dynamic load-carrying capacity for endurance fatigue **is about 600 MPa, which is equivalent to a compressive loading of about 6000 bar. That means pressure-bearing parts exposed to repeated loading of 600-700 MPa cannot exhibit **endurance strength **(see *Fig. 3*). However it is possible, using suitable measures described below, to optimize endurance vibration strength, thereby maximizing service life.

* Fig. 3: Vibrational stress endurance as shown by a Wöhler diagram*

**Low-cycle endurance:**Stress amplitudes at which damage (breakage) occurs with N < 10³ alternating loads**Static strength:**Stress amplitudes at which damage (breakage) occurs with 10³ < N < 10^{6}alternating loads**Endurance strength:**Stress amplitudes at which damage (breakage) does not occurs with any number of alternating loads, 2 x 10^{6}≥ N ≥ 10^{7}

Favorable **design measures **and carefully selected **post-treatment of the measuring body **can have a positive effect on its fatigue life, thereby extending its service life. The following influence quantities are relevant:

**Type of vibrational stress****Ambient influences****Material and its condition****Geometry of the measuring body**

### 2.2 Type of vibrational stress / ambient influence

The type of vibrational stress is generally identified, depending on the application, as **repeated or alternating loading **Therefore it cannot be influenced or if so then only slightly. **Ambient influences** such as increased temperature have a negative effect on fatigue, similar to other stability parameters. **Corrosive media** also have a detrimental effect on fatigue life, resulting in the **elimination of the horizontal branch of the Wöhler curve** (see *Fig. 3*). The endurance strength range is characterized by an **asymptotic curve**.

### 2.3 Material and measuring body design

**Selecting materials** for transducer construction always involves a **compromise between maximum service life under dynamic loading and the metrological properties to be achieved (in the spring elements)**. By no means are all steels that appear to be excellent materials for high pressure applications due to a high yield point or some other such consideration are also ideally suited as material for the measuring body. Especially **unsuitable spring properties** in connection with **too large a hysteresis** result in **accuracy that cannot be used**. Accordingly they are not considered for transducer construction. Commonly used spring element materials have a tensile strength of > 1GPa, which makes them suitable for high pressure metrological applications.

**Spring measuring bodies with a tube-like shape** have proven to be an excellent **hollow body design** (see *Fig. 4*).

*Fig. 4: Stress state / measuring body in hollow body design*

High pressure transducers are generally designed as "**thick-walled tubes**". Especially noteworthy in the design is the **special strain response **due to **uneven distribution of stress over the cross section of the tube**. Figure 4 shows that the **internal fiber of the pressure hole** with its triaxial stress state is the **point subjected to the highest loading**. The greatest load on the internal fiber occurs in the tangential direction (σt). The loading involved is tensile stress. The external fiber with its biaxial stress state is also exposed to stresses, but they are much lower.

Due to the **multi-axial stress state **on the internal fiber, the **equivalent reference stress** (σv) postulated by strength theory has to be considered and correlated with the corresponding material characteristic value. The **pressure hole **corresponds to the diameter *Di* while the external diameter *Da* corresponds to the external dimensions of the measuring body (see *Fig.4*). The** ideal diameter ratio for the hollow body design** is 2-4.

When the **pressure transducer is used in the ultra-high pressure range **≥ 1 GPa, that does not mean that the measuring body will be torn apart by the enormous peak tensile stresses on the internal fiber of the measuring body. The internal tube pressure is indeed at the yield point, but the outer layers of the measuring body around the edges still bear the pressure very well. If the pressure is increased still further, the place at which the yield point is exceeded moves slowly outward. Breakage does not occur until the yield point has moved to the outermost layer. The design of the measuring body is balanced with the thickness of the wall (*Da/Di*) designed so that the maximum dynamic properties of the spring steel used, and thus the **maximum capacity for load changes** is reached. It should be noted in this regard that for a pressure of about 700 MPa or more, increasing the thickness of the wall does not contribute to increasing dynamic strength. All** influencing material factors that reduce tensile strength**, such as notches, inclusions and a high level of surface roughness at points in the measuring body subject to high pressure loading, lead to **lower tensile strength overall and with it a shorter service life**.

The pressure chamber in the measuring body design used by HBM is **monolithically enclosed**. That means the measuring body including the pressure connection part is made of one solid piece, a single measuring body **without any additional welding seams**. The special monolithic measuring body design is optimized in all respects and completely eliminates abrupt transitions in cross-section (notch effect) and welding seams, which shorten service life. Welding seams represent a significant risk under high pressures due to the high notch effect on the welding seam root. They also limit the number of possible load cycles, which adversely affects service life. The optimized monolithic measuring body design is especially low in stress gradients and peaks. The measuring body is furthermore designed so that additional stresses are minimized, especially in the critical tangent direction, which has a positive effect on vibration strength.

*Fig. 5: Different measuring bodies in monolithic hollow-body design*

### 2.3.1 Strain hardening by means of autofrettage

**Post-treatment of the pressure measuring body based on the autofrettage method** improves **vibration strength**, especially in the high pressure range. In this process the **internal pressure is raised to the yield point of the internal fibers** and then slowly increased still further. When the internal pressure then returns **to zero**, the inside wall retains a **plastic deformation**. The** internal stresses** resulting from this process are expressed in the form of **compressive stress**. This means that the tensile stress peak on the critical internal fiber is transformed so that the internal fiber constitutes a negative compressive stress in a depressurized state (see *Fig. 6*).

Fig. 6: Schematic voltage curve after autofrettage

If the **measuring body is then exposed to internal pressure**, the compressive stress counteracts the tensile stress to the extent that it is practically depleted. In this equilibrium of pressure and stress, the **remaining stress is then reduced by the amount of compressive stress**. In addition, the **surface roughness is reduced to a minimum** through **partial plastification**. This process of strain hardening by selectively introducing internal compressive stresses** increases vibration strength**, thereby extending **service life** under dynamic stress. **Maximum vibration strength and the longest possible service life **can be achieved by combining the optimized monolithic measuring body design without welding seams and the autofrettage process.

## 3. Portfolio

Various pressure transducers are available from HBM for **measuring ranges up to 15,000 bar **(see* Fig. 7*). The individual series differ mainly in their** design, measuring ranges and achievable measurement accuracy**. Pressure transducers of the P2V series include transducers with an** integrated measuring amplifier**. They can** optionally **make an **analog output with current or voltage **available.

*Fig. 7: High pressure transducers*

Pressure transducers from HBM are typically used in applications where attributes such as long **service life, robustness and accuracy** are prime considerations. The application areas extend from diverse measurement tasks in **hydraulics** and general **mechanical engineering** to** test bench **applications and beyond to reference transducers in **metrological institutes**.

**Typical application areas are:**

- Water jet cutting
- Autofrettage of components
- High-pressure sterilization of foodstuffs
- Internal high pressure forming (IHF)
- Test bench applications (diesel injection technology)
- Metrological institutes

## 4. Summary

**Pressure transducers with strain gauge technology **and a monolithic measuring body design are ideally suited for high-pressure measurement technology. The** foil strain gauge principle **allows for a perfect selection and **optimization of measuring body geometry**, as the SG is not applied until the last step. The **monolithic measuring body design** together with** optimized manufacturing steps** and** post-treatment** (strain hardening by means of autofrettage) ensure not only that a very high precision class is achieved, but also for high resistance to **alternating loads and a long service life**. All three parameters are crucially important in high-pressure measurement technology. The very **robust design** and the associated** long service life **of these pressure transducers represent an important contribution in terms of **extending service life **in technical applications.

Advantages of HBM pressure transducers:

- Very high accuracy
- High resistance to alternating loads
- Monolithic measuring body
- Very robust
- Static and dynamic pressures
- Insensitive to pressure peaks

*SG = strain gauge