Advances in traceable calibration of cylinder pressure transducers

The VTT MIKES dynamic pressure primary measurement standard is built on a frame of a commercial AVL B620-type drop weight secondary dynamic pressure calibrator. Instead of using reference transducers, traceable impact pressure is obtained through measurement of impact acceleration, and predetermined impact mass and area of the piston-cylinder assembly.

The measurement sequence starts by lifting the drop weight up to a certain height using an electromagnet and a lifting mechanism. This height determines the impact force and thus the amplitude of the pressure pulse. As the drop weight is released, it falls along the guiding rods (figure 1). When the impact hammer of the drop weight (figure 3) hits the piston (figure 4), the liquid inside the fluid cavity (figure 4) is squeezed and a pressure pulse (figure 9) is created. After the pressure pulse, the drop weight jumps off the piston. A pneumatic lifting mechanism (figure 1) lifts the drop weight up until the electromagnet catches the drop weight again.

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In figure 2, the design and signal flow chart of the measurement setup is shown. The sampling frequency of the 10 MHz interferometer signal in a heterodyne Michelson type interferometer setup is 250 MHz. In order to limit the amount of analyzed acceleration signal, the collection of the data is triggered when the piston comes in contact with the impact hammer. A couple milliseconds of pre-trigger data is also collected (figure 5). The displacement data measured by the interferometer setup is analyzed in a LabVIEW program. Based on the displacement data, the acceleration of the weight as a function of time is calculated (figures 5–7). Finally, the impact pressure is calculated based on the acceleration, the mass of the drop weight and the effective area of the piston-cylinder assembly. The output signal of the transducer under calibration is converted to a digital signal using a data acquisition unit (DAQ). In some cases, the transducer signal needs to be amplified before the DAQ. The sampling frequencies of dynamic pressure transducers are typically 500 kHz.

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As the impact inevitably creates disturbing mechanical vibrations, special care is taken to attach the device firmly. The device is fixed to a granite block which in turn is firmly attached to the laboratory floor. Even though all components are attached with screws, vibrations occur. These vibrations in turn create the main technical challenge for measuring the impact force. In practice, tilting and vibration of the drop weight easily lead to ambiguity of the measured impact force because of changing friction and stick-slip phenomenon, which can be described as a kind of jerking motion between linear guides and guiding rods. Therefore, tilting and vibrations of the drop weight needs to be minimized in order to reliably measure the impact force.

In the previous design of the measurement standard, the displacement was measured at only one point of the drop weight. To develop the dynamic pressure measurement standard further, a new drop weight and an interferometer setup was developed. A dual beam Michelson interferometer setup was applied to enable displacement measurements at two points at opposite corners of the weight (figure 1). As a result, the tilt of drop weight can be monitored during impact.

The new drop weight with a mass of 3.6 kg is lighter than the previous 12.6 kg drop weight in order to extend pressure range downwards. To reduce the vibrations and tilt of the weight, suitable linear guides were machined in the house (marked as green in figure 3). Tightening the linear guide screws (blue screws in figure 3) squeezes the linear guides, and consequently reduces the gap between the linear guides and the guiding rods. In this way, the gap between the guides and the guiding rods can be optimally adjusted. In order to further reduce vibrations and stick-slip phenomenon, 1 mm rubber film (small red plate in figure 3) was installed on top of the impact hammer to reduce vibrations and stick-slip phenomenon.

In order to calibrate transducers at high-temperatures typical for combustion engine-type environments, a heating option for the measurement head was designed at VTT MIKES. It has been estimated [10] that dynamic pressure transducers should be tested in around 200 $^\circ \rm C$ temperature to imitate temperatures inside a diesel engine. In this design, the fluid near the transducer as well as transducer's sensing element are heated using a resistive heating wire (figure 4). Silicone oil designed for oil baths is used as the working fluid inside the cavity.

When the screws in the linear guides are tightened, the guides expand such that the gap between the linear guides and the guiding rods decreases. As a result, the friction increases and the acceleration of the drop weight in free fall decreases. Although the friction causes an external force, the calibration results are unaffected. This is due to fact that the impact force is determined based on the change in acceleration caused by impact. A constant additional frictional force will therefore not influence the change in acceleration. Even in the extreme case where the drop weight did not start to slide down on its own, but needed assisted initial velocity, observed changes in the calibration results were less than 0.2%, which is within the experimental repeatability.

If the acceleration before impact is not measured and accounted for, the calibration results will not be reliable. This is especially important in the lower end of the pressure range, where the relative contribution of the frictional forces become significant.

As discussed in [17], at the moment of maximum pressure, eccentric impact between impact hammer and piston creates friction between piston (figure 4) and cylinder (figure 1). This friction reduces the force carried by piston at the moment of maximum pressure. This effect can be observed by changing the placement of measurement head, which changes the point of impact between impact hammer and piston. In case of perfectly positioned impact with no eccentricity, friction between piston and cylinder during maximum pressure is negligible.

Ideally, the acceleration of the center of mass during impact should be measured, as mentioned before. Similar to [18], the error caused by measuring the acceleration from drop weight was estimated using FEM-simulations (figure 8). Simulations indicate that the error varies from 0.1% to 3.0% depending on the pressurized medium and the construction of the drop weight. Compressibility of the pressurized medium varies between different liquids and depends on the amount of air bubbles in the liquid. This variation in compressibility also changes the duration of impact. The duration of the impact and pressure pulse can vary as much as from 3 ms to 7 ms. As the duration of the impact changes, the amplitudes of different vibration modes changes and the acceleration difference between the center of mass and measurement points changes. By carefully filling the measurement chamber to avoid entrapment of air bubbles, the pressure pulse duration can be well controlled, and it is typically around 4 ms.

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Experimental studies were performed to investigate the influence of impact mass deformation. The construction of the drop weight was modified for these studies using additional plate weights. This modification not only increased the mass to 17 kg, but also changed the center of mass and made the construction stiffer, and thus rendered the vibrational modes of the weight. Measurements with the additional plate weights resulted in a 2.5% decrease in the measured sensitivity of the transducer. According to simulations, the corresponding value was 2.0%. Simulations indicate that the change in the measurement results is mostly due to the reduced bending of drop weight (figure 8). The stiffer construction implies that, the acceleration of the center of mass and the measured acceleration is practically the same. The half- percent difference between the simulations and experimental measurements is most probably due to the attachment of the plate weight. In simulations, an integral rigid weight was assumed, but in reality, the plate weight was attached with 3 screws.

Currently, glycerol or silicon oil is used as a pressurized medium. Glycerol is used at room temperatures and silicon oil at higher temperatures. No differences in the calibration results have been observed when comparing calibrations performed with different liquids. If differences exists, they are considerably smaller than the spread of measurement results and cannot be detected. Therefore our experience agrees with an argument presented in [17]: Viscous resistance of pressurized medium does not cause considerable pressure losses during moment of maximum pressure because velocity of drop weight, piston and pressurized medium is approximately zero. Consequently, similar to [2], it is assumed that the liquid media does not cause any significant pressure losses at the moment of maximum pressure.

Experiments also support calibration results are not influenced by a small amount of air bubbles in the liquid. Moreover, the dimensions of the cavity are orders of magnitude smaller than the wavelength of the pressure pulse, and thus the pressure inside the cavity is considered uniform. As discussed in [19], aforementioned issues might become a challenge in larger cavity volumes, more compressible transmission media and higher dynamic pressure signal frequencies.

Similarly, negligible changes in calibration results have been observed if the stiffness of the system is decreased by adding more rubber on the impact hammer. In extreme case of 7 mm rubber tip on the impact hammer, around 0.3% change was noticed, which is still within the experimental repeatability. Normally, around 1 mm thick rubber tip is used.

The combined relative measurement uncertainty of calibration ${\left. {u\left( {\text{C}} \right)} \right|_{\text{p}}}$ can be calculated according to the law of propagation of uncertainties [20] and assuming uncorrelated input quantities as follows:

$$\begin{align}{\left. {{u^2}\left( C \right)} \right|_p} = & u_r^2\left( {{m_{tot}}} \right) + u_r^2\left( A \right) + u_r^2\left( {{a_b}} \right) + u_r^2\left( {{a_v}} \right) + u_r^2\left( {{a_t}} \right) \nonumber\\ & + u_r^2\left( {{a_f}} \right) + u_r^2\left( {{a_d}} \right)\end{align} \tag{ 2 }$$

in which ${u_r}\left( {{m_{tot}}} \right)$ is the uncertainty of mass including drop weight, piston and pressurized medium, ${u_r}\left( A \right)$ is the uncertainty of piston-cylinder effective area, u_r(${{\text{a}}_{\text{b}}}$) is the uncertainty in acceleration measurement due bending and deformation of the impact mass, u_r(${{\text{a}}_{\text{v}}}$) is the uncertainty in acceleration measurement caused by vibrational noise, u_r(${{\text{a}}_{\text{t}}}$) is the uncertainty in acceleration measurement due to tilt of drop weight,${\text{ }}u({{\text{a}}_{\text{f}}}$) is the uncertainty in acceleration measurement due to friction between piston and cylinder due to eccentric impact and $u({{\text{a}}_{\text{d}}}$) is the uncertainty in acceleration measurement due to the dispersion of measurement results.

Uncertainty of mass ${u_r}\left( {{m_{tot}}} \right)$ includes the weighing uncertainty, as well as the ambiguity of mass caused by the trigger electrical cord attached to the drop weight [3]. As the uncertainty of weighing of the drop weight and piston is rather small, their effect can be ignored. The electrical cord of the drop weight swings freely during impact, and thus its effect is hard to estimate. Effect was estimated by swinging the cord on top of the mass balance. However, the mass of the electrical cord is less than 0.1% of the total impact mass and therefore it has only a minimal effect on the overall uncertainty. The uncertainty of mass of the pressurized medium is the largest component related to uncertainty of mass. This is because a small amount of fluid leaks out of the chamber at each impact. Anyhow, the uncertainty of mass is rather small compared to other uncertainty sources (table 1).

Table 1. Uncertainty budget for a dynamic pressure transducer calibration at 7 MPa and 120 $^\circ \rm C$.

Uncertainty component	Source of uncertainty	Standard relative uncertainty/%
${u_r}({m_{tot}}$)	Mass of drop weight, piston, pressurized medium and electrical cord	0.1
${u_r}$ (A)	Effective area of piston-cylinder	0.1
${u_r}$ (${{\text{a}}_{\text{b}}}$)	Bending and deformation of drop weight	0.8
${u_r}$ (${{\text{a}}_{\text{v}}}$)	Vibration induced noise	0.2
${u_r}$ (${{\text{a}}_{\text{t}}}$)	Tilt of drop weight	0.1
${u_r}$ (${{\text{a}}_{\text{f}}}$)	Friction between piston and cylinder	0.4
${u_r}$ (${{\text{a}}_{\text{d}}}$)	Dispersion of transducer output	0.4
Combined standard uncertainty (k = 1)		1.0
Expanded uncertainty (k = 2)		2.0

Uncertainty of the effective area ${u_r}\left( A \right)$ of the piston-cylinder assembly includes uncertainties of the dimensional measurements and spatial variations of the piston projected area, as well as the pressure dependency of the effective area. The uncertainty due to these effects is less than 0.05% at room temperature [3]. If heating is applied, the piston-cylinder assembly expands due to increased temperature. As the temperature may vary spatially in the piston-cylinder assembly, it is difficult to exactly estimate the change in the effective area. Therefore, a worst-case estimate of the maximum change is applied and added to the uncertainty budget. Even then, the effect of temperature in the range 20 $^\circ \rm C$—200 $^\circ \rm C$ is smaller than 0.02%. Thus, the uncertainty of the effective area has only a minor effect on the overall uncertainty (table 1).

The most significant uncertainty sources are related to measurement of the maximum acceleration of the drop weight. These include uncertainty of acceleration due to bending and deformation of the impact mass u_r(${{\text{a}}_{\text{b}}}$), uncertainty caused by vibration induced noise u_r(${{\text{a}}_{\text{v}}}$) and uncertainty due to tilt of drop weight u_r(${{\text{a}}_{\text{t}}}$). As discussed earlier, deformation of the mass results in an error in the acceleration measurement. This is because the point of measurement does not correspond to the center of mass of the impact weight. The FEM model is used to correct for this error. The uncertainty u_r(${{\text{a}}_{\text{b}}}$) of this correction term is the most significant component in the overall measurement uncertainty (see table 1). The uncertainty due to vibration induced noise in the acceleration signal u_r(${{\text{a}}_{\text{v}}}$) is estimated as in [3] by plotting the amplitude of the measured maximum acceleration as a function of low-pass filter cut-off frequency and investigating changes in the neighborhood of the applied cut-off frequency (2 kHz). This procedure is applied for both interferometric measurements and the resulting uncertainties are included in the overall standard uncertainty. The uncertainty due to tilting of the drop weight during impact u_r(${{\text{a}}_{\text{t}}}$) is roughly estimated based on the difference between the acceleration signals measured from the front and back mirrors (see figure 6). Besides the aforementioned uncertainty sources, the uncertainty due to the coaxial alignment of the laser beam with the piston was also considered. Because of careful alignment of the laser, this uncertainty becomes negligible and is therefore not included in the overall uncertainty [3].

Uncertainty in acceleration measurement due to friction between the piston and the cylinder $u({{\text{a}}_f}$) is created by an eccentric impact between the impact hammer and the piston [17]. The gap between the piston and the cylinder is considered well lubricated and contact length is around 2 cm. However, in our drop weight device, point of impact between the impact hammer and the piston is hard to orient within 1 mm. Therefore, using the formula in [17], uncertainty in acceleration measurement due to friction between the piston and the cylinder is considered conservatively to be around 0.4%. Uncertainty due to dispersion of the measurement results u_r(${{\text{a}}_{\text{d}}}$) includes the spread of the peak pressure readings from the measurement standard and transducer under calibration. This uncertainty component will greatly depend on the spread of the transducer outputs under calibration and is typically between 0.2% and 1.2%. Spread from measurement standard is mostly caused by tilt of drop weight during impact and is typically in the order of 0.4%.