Vibrating beam accelerometer with pressure damping

A system for determining acceleration, the system comprising:

• a pendulous mass vibrating beam accelerometer (VBA), comprising:
• a support base that defines a first plane;
• a resonator comprising an anchored portion and a released portion, wherein the anchored portion of the resonator mechanically connects to the support base;
• a pendulous proof mass mechanically connected to the released portion of the resonator;
• one or more damping combs comprising movable comb fingers and anchored comb fingers,
• wherein the anchored comb fingers of the one or more damping combs are mechanically connected to the support base,
• wherein the movable comb fingers of the one or more damping combs are mechanically connected to the proof mass, and
• wherein a spacing between the movable comb fingers of the one or more damping combs and the anchored comb fingers of the one or more damping combs is configured to provide air damping for the proof mass;
• and
• a resonator connection structure mechanically connected to the support base with an anchor, wherein the resonator connection structure is in a second plane parallel to the first plane;
• a hinge flexure configured to connect the pendulous proof mass to the resonator connection structure, wherein the hinge flexure suspends the pendulous proof mass parallel to the support base at the anchor, and wherein the pendulous proof mass rotates about the hinge flexure in the second plane in response to an acceleration of the system parallel to the first plane of the support base,
• wherein the resonator is configured to connect the pendulous proof mass to the resonator connection structure and to flex in the second plane based on a rotation of the pendulous proof mass about the hinge flexure,
• wherein the pendulous proof mass, the hinge flexure, the resonator connection structure and the resonator are in the second plane,
• a single pressure cavity, wherein the single pressure cavity contains the support base, the resonator, the pendulous proof mass, the resonator connection structure and the one or more damping combs at a same pressure;
• a resonator driver circuit operatively connected to the pendulous mass VBA;
• and
• processing circuitry operatively connected to the pendulous mass VBA via the resonator driver circuit, wherein:
• the resonator driver circuit is configured to output a first signal that causes the resonator of the pendulous mass VBA to vibrate at a respective resonant frequency of the resonator,
• an acceleration of the pendulous mass VBA in a direction substantially parallel to the second plane causes a rotation of the pendulous proof mass about the hinge flexure parallel to the second plane,
• the resonator is configured to receive a force, in response to the rotation of the pendulous proof mass, such that the force causes a respective change in resonant frequency of the resonator, and
• the processing circuitry is configured to receive a second signal from the pendulous mass VBA indicative of a respective change in the resonant frequency and based on the respective change in resonant frequency, determine an acceleration measurement,
• wherein the pendulous proof mass includes support flexures with anchor portions and flexible portions, the anchor portions being configured to not exert significant forces on the pendulous proof mass such that the pendulous proof mass is connected to the support base primarily by the anchor and the resonator connection structure is configured such that the resonator connection structure prevents bias errors that result from a thermal expansion mismatch between the support base and the pendulous proof mass and the resonator.

A method comprising:

• receiving, by processing circuitry, one or more electrical signals indicative of a frequency of a first resonator beam and a frequency of a second resonator beam from a vibrating beam accelerometer (VBA), wherein the VBA comprises:
• a support base defining a first plane;
• a resonator comprising an anchored portion and a released portion, wherein the anchored portion of the resonator mechanically connects to the support base;
• a pendulous proof mass mechanically connected to the released portion of the resonator;
• one or more damping combs comprising movable comb fingers and anchored comb fingers,
• wherein the anchored comb fingers of the one or more damping combs are mechanically connected to the support base,
• wherein the movable comb fingers of the one or more damping combs are mechanically connected to the proof mass, and
• wherein a spacing between the movable comb fingers of the one or more damping combs and the anchored comb fingers of the one or more damping combs is configured to provide air damping for the proof mass;
• and
• a resonator connection structure mechanically connected to the support base with an anchor, wherein the resonator connection structure is in a second plane parallel to the first plane;
• a hinge flexure configured to connect the pendulous proof mass to the resonator connection structure, wherein the hinge flexure suspends the pendulous proof mass parallel to the support base at the anchor, and wherein the pendulous proof mass rotates about the hinge flexure in the second plane in response to an acceleration of the VBA parallel to the first plane of the support base,
• wherein the resonator is configured to connect the pendulous proof mass to the resonator connection structure and to flex in the second plane based on a rotation of the pendulous proof mass about the hinge flexure,
• wherein the pendulous proof mass, the hinge flexure, the resonator connection structure and the resonator are in the second plane,
• a single pressure cavity, wherein the single pressure cavity contains the support base, the resonator, the pendulous proof mass, the resonator connection structure and the one or more damping combs at a same pressure;
• determining, by the processing circuitry and based on the one or more electrical signals, the frequency of the first resonator beam and the frequency of the second resonator beam;
• and
• calculating, by the processing circuitry and based on the frequency of the first resonator beam and the frequency of the second resonator beam, an acceleration of the VBA,
• wherein the pendulous proof mass includes support flexures with anchor portions and flexible portions, the anchor portions being configured to not exert significant forces on the pendulous proof mass such that the pendulous proof mass is connected to the support base primarily by the anchor and the resonator connection structure is configured such that the resonator connection structure prevents bias errors that result from a thermal expansion mismatch between the support base and the pendulous proof mass and the resonator.