Method and apparatus for an absolute precision load gauge

A method for precisely calculating an applied load directly in units of mass or force comprising the steps of:

• a. Providing
• i. a load carrying member (LCM) to which a load to be measured will be applied;
• ii. a digital acquisition load-calculating computer;
• iii. an ultrasonic transducer connected to the computer and positioned to generate ultrasonic waves into the LCM and receive reflected waves;
• iv. a linear displacement probe connected to the LCM;
• b. determining with respect to the LCM at zero load and at Reference Temperature:
• i. lateral dimension,
• ii. cross-sectional area,
• iii. the density of the load carrying member (LCM), and
• iv. recording the reference temperature;
• c. determining at zero load round trip times between opposite interior surfaces of the LCM of:
• i. a longitudinal ultrasound wave, a vertically polarized ultrasound shear wave and a horizontally polarized ultrasound shear waves, all propagating laterally in the direction perpendicular to the applied vertical loading direction by generating with the ultrasonic transducer a longitudinal ultrasound wave, a vertically polarized ultrasound shear wave and a horizontally polarized ultrasound shear waves, all propagating laterally in the direction perpendicular to the applied vertical loading direction;
• ii. recording ambient temperature and lateral dimensional change at which these round trip times are measured;
• d. determining with the load to be measured applied to the LCM the round trip times between opposite interior surfaces of the LCM of:
• i. a longitudinal ultrasound wave, a vertically polarized ultrasound shear wave and a horizontally polarized ultrasound shear waves, all propagating laterally in the direction perpendicular to the applied vertical loading direction by generating with the ultrasonic transducer a longitudinal ultrasound wave, a vertically polarized ultrasound shear wave and a horizontally polarized ultrasound shear waves, all propagating laterally in the direction perpendicular to the applied vertical loading direction;
• ii. recording
• a. ambient temperature;
• and
• b. determining lateral dimensional change at which these round trip times are measured with the linear displacement probe:
• e. determining with the computer the applied load to be measured from equations derived from application of finite deformation theory, thermodynamics of finite deformation of elastic solids and nonlinear elastic equations of state of solids under uniaxial homogeneous loading and with the values determined at a., b., c. and d. above by:
• i. converting the adiabatic SOEC (second order elastic constants) and mixed TOEC (third order elastic constants) into isothermal values;
• ii. calculating thermodynamic stress τ33;
• iii. calculating the third order elastic constants;
• iv. calculating principal horizontal stretch λ1 and principal vertical stretch λ3;
• v. calculating Cauchy stress σ33;
• and
• vi. calculating applied load P from the values derived at f. i., ii., iii, iv., and v. above.