A Modified Model for the Temperature Effect-Induced Error in Hydrostatic Leveling Systems

To investigate systematically how the temperature effect influences the measurement accuracy of a hydrostatic leveling system (HLS), ambient-temperature and temperature-gradient test platforms were built in the laboratory. The temperature of each measuring point of the HLS was collected by a high-precision temperature sensor, and the influences of the ambient temperature
${T}_{\mathrm {A}}$
, temperature gradient
${T}_{\mathrm {G}}$
, heating/cooling rate, communicating-pipe expansion coefficient, and measuring-point distance
${D}_{\mathrm {test}}$
on the HLS measurement accuracy were analyzed quantitatively. The results show that the error of the two-HLS setup was caused by the expansion of the communicating pipe and the liquid between the datum point and the measuring point both under ambient-temperature and temperature-gradient conditions. The relative ambient-temperature influence coefficient
$\Delta {P}$
and temperature gradient influence coefficient
$\Delta {P}_{\mathrm {t-G}}$
, respectively, had a linear correlation with the difference between the expansion coefficients of the communicating liquid and pipe (
$\gamma _{\mathrm {di}} - \gamma _{\mathrm {pi}}$
). Moreover,
$\Delta {P}_{\mathrm {t-A}}$
and
$\Delta {P}_{\mathrm {t-G}}$
had a negative power relationship with
${D}_{\mathrm {test}}$
for given communicating pipe and liquid. A temperature-modified model was developed theoretically based on test results, and its reliability was verified via on-site tests.