Resonator temperature transducer

Resonator temperature measuring apparatus comprising

• a pair of elongate, spaced-apart generally parallel bars coupled together at one end, each having a thickness t and width w, with the distance from the location at which the bars are coupled together to the free ends of the bars being m, said bars comprised of piezoelectric material with the crystallographic axes oriented such that when the bars are stimulated to vibrate in the torsional mode 180 degrees out of phase, the frequency of vibration varies as a function of the temperature to which the bars are exposed,
• a support structure to which the joined ends of the bars are attached, where the distance from the support structure to the free ends of the bars is L,
• electrodes placed on the bars and responsive to oscillatory signals for causing the bars to resonate in the torsional mode 180 degress out of phase,
• means for applying oscillatory signals to said electrodes to cause the bars to resonate in the torsional mode at a frequency f.sub.T,
• means for producing an oscillatory signal having frequencies which follow the frequency of vibration of the bars, and
• wherein t, w, m and L are selected so that the following representations do not approach within about three percent of equaling one or two:
• ##EQU7## where A.sub.an =3.05, 18.99, 51.92 for n=1, 2 and 3
• A.sub.bn =8.57, 41.82, 96.97 for n=1, 2 and 3
• A.sub.pn =3.91, 22.12, 59.09, 114.1, 189.9, 281.8 for n=1, 2, 3, 4, 5 and 6
• A.sub.wn =4.96, 30.91, 71.82, 89.80, 143.4, 180.8 for n=1, 2, 3, 4, 5 and 6 ##EQU8## f.sub.an, f.sub.pn, f.sub.bn and f.sub.wn are the frequencies of vibration of spurious modes of the transducer, where n is the order of the mode, P is the density of the material and S.sub.55 and S.sub.66 are shear compliances and E is Young's Modulus of the material.

A resonator temperature transducer comprising

• a pair of elongated, generally parallel bars coupled together at one end, said bars each having a thickness t and width w, with the distance from the location at which the bars are coupled together to the free ends of the bars being m, and said bars being made of quartz crystal with the crystallographic axes oriented so that when the bars are caused to vibrate in the torsional mode, the frequency of vibration varies as a function of temperature,
• an enlarged mounting section joined to the bars at said one end, with the distance from the mounting section to the free ends of the bars being L,
• means for causing said bars to vibrate in the torsional mode 180.degree. out of phase at a frequency f.sub.T, and
• wherein t, w, m and L are selected so that
• 0.2.ltoreq.t/w.ltoreq.0.5,
• 10.ltoreq.m/w.ltoreq.16
• 1.35.ltoreq.L/m.ltoreq.1.45, and
• f.sub.T /f.sub.p4 .noteq.1, f.sub.T /f.sub.a2 .noteq.1, f.sub.T /f.sub.w5 .noteq.1,
• where ##EQU9## E is Young's Modulus of the material, and P is the density of the material.

The resonator temperature transducer comprising

• a pair of elongated, generally parallel bars coupled together at one end, said bars each having a thickness t and width w, with the distance from the location at which the bars are coupled together to the free ends of the bars being m, and said bars being made of quartz crystal with the crystallographic axes oriented so that when the bars are caused to vibrate in the torsional mode, the frequency of vibration varies as a function of temperature,
• an enlarged mounting section joined to the bars at said one end, with the distance from the mounting section to the free ends of the bars being L,
• means for causing said bars to vibrate in the torsional mode 180.degree. out of phase at a frequency f.sub.T, and
• wherein t, w, m and L are selected so that
• 0.4.ltoreq.t/w.ltoreq.0.8,
• 12.ltoreq.m/w.ltoreq.18,
• 1.35.ltoreq.L/m.ltoreq.1.45, and
• f.sub.T /f.sub.p4 .noteq.1, f.sub.T /f.sub.a3 .noteq.1, f.sub.T /f.sub.b3 .noteq.1,
• where ##EQU11## E is Young's Modulus of the material, and P is the density of the material.

Resonator temperature measuring apparatus comprising

• a pair of elongate, spaced-apart, generally parallel bars coupled together at one end, said bars each having a thickness t and width w, with the distance from the location at which the bars are coupled together to the free ends of the bars being m, said bars comprised of a piezoelectric material with the crystallographic axes oriented so that when the bars are caused to vibrate in the torsional mode, the frequency of vibration varies as a function of temperature,
• an enlarged mounting section formed integral with the bars at said one end, with the distance from the mounting section to the free ends of the bars being L,
• means for causing said bars to vibrate in the torsional mode 180.degree. out of phase at a frequency f.sub.T,
• means for providing an indication of the frequency of vibration of th bars,
• wherein t, w, m and L are selected so that the following ratios do not approach with about three percent of equaling one or two:
• f.sub.T /f.sub.an, f.sub.T /f.sub.pn, f.sub.T /f.sub.bn, and f.sub.T /f.sub.wn, and wherein m and L are further selected so that 1.1.ltoreq.L/m.ltoreq.1.5,
• where ##EQU13## A.sub.an =3.05, 18.99, 51.92 for n=1, 2 and 3 A.sub.bn =8.57, 41.82, 96.97 for n=1, 2 and 3
• A.sub.pn =3.91, 22.12, 59.09, 114.1, 189.9, 281.8 for n=1, 2, 3, 4, 5 and 6
• A.sub.wn =4.96, 30.91, 71.82, 89.80, 143.4, 180.8 for n=1, 2, 3, 4, 5 and 6 ##EQU14## f.sub.an, f.sub.pn, f.sub.bn and f.sub.wn are the frequencies of vibration of spurious modes of the transducer, where n is the order of the mode, P is the density of the material and S.sub.55 and S.sub.66 are shear compliances and E is Young's Modulus of the material.