Spurious mode map for DETF force transducer

A double ended tuning fork (DETF) comprising:

• a pair of spaced apart vibrating beams, generally parallel and joined together at opposing ends, each beam having a thickness t, width w, length m, said DETF having a length L wherein the dimensions for t, w, m and L are selected using a finite element model to satisfy the following relationship:
• ##EQU31## where K.sub.f/fp1 (A,B).noteq.1;
• A=t/w;
• B=L/m and S is the sensitivity ofthe DETF over a predetermined operating range and the coefficient K(A,B) is selected using a polynomial curve fitting technique to fit the following equation over a predetermined dimensional range:
• K.sub.f/fmn =b.sub.0 +b.sub.1 *B+b.sub.2 *B.sup.2 +b.sub.3 *B.sup.3 +a.sub.1 *A
• where K.sub.f/fmn are the fundamental to spurious mode ratios and the coefficients a and b are determined for each K.sub.f/fmn over the predetermined dimensional range.

A double ended tuning fork (DETF) comprising:

• a pair of spaced apart vibrating beams, generally parallel and joined together at opposing ends, each beam having a thickness t, width w, length m, said DETF having a length L wherein the dimensions for t, w, m and L are selected using a finite element model to satisfy the following relationship:
• ##EQU32## where K.sub.f/fp2 (A,B).noteq.1;
• A=t/w;
• B=L/m and S is the sensitivity of the DETF over a predetermined operating range and the coefficient K(A,B) is selected using a polynomial curve fitting technique to fit the following equation over a predetermined dimensional range:
• K.sub.f/fmn =b.sub.0 +b.sub.1 *B+b.sub.2 *B.sup.2 +b.sub.3 *B.sup.3 +a.sub.1 *A
• where K.sub.f/fmn are the fundamental to spurious mode ratios and the coefficients a and b are determined for each K.sub.f/fmn over the predetermined dimensional range.

A double ended tuning fork (DETF) comprising:

• a pair of spaced apart vibrating beams, generally parallel and joined together at opposing ends, each beam having a thickness t, width w, length m, said DETF having a length L wherein the dimensions for t, w, m and L are selected using a finite element model to satisfy the following relationship:
• ##EQU33## where K.sub.f/fp2 (A,B).noteq.1;
• A=t/w;
• B=L/m and S is the sensitivity of the DETF over a predetermined operating range and the coefficient K(A,B) is selected using a polynomial curve fitting technique to fit the following equation over a predetermined dimensional range:
• K.sub.f/fmn =b.sub.0 +b.sub.1 *B+b.sub.2 *B.sup.2 +b.sub.3 *B.sup.3 +a.sub.1 *A
• where K.sub.f/fmn are the fundamental to spurious mode ratios and the coefficients a and b are determined for each K.sub.f/fmn over the predetermined dimensional range.

A double ended tuning fork (DETF) comprising:

• a pair of spaced apart vibrating beams, generally parallel and joined together at opposing ends, each beam having a thickness t, width w, length m, said DETF having a length L wherein the dimensions for t, w, m and L are selected using a finite element model to satisfy the following relationship:
• ##EQU34## where K.sub.f/fp3 (A,B).noteq.1;
• A=t/w;
• B=L/m and S is the sensitivity of the DETF over a predetermined operating range and the coefficient K(A,B) is selected using a polynomial curve fitting technique to fit the following equation over a predetermined dimensional range:
• K.sub.f/fmn =b.sub.0 +b.sub.1 *B+b.sub.2 *B.sup.2 +b.sub.3 *B.sup.3 +a.sub.1 *A
• where K.sub.f/ fmn are the fundamental to spurious mode ratios and the coefficients a and b are determined for each K.sub.f/fmn over the predetermined dimensional range.

A double ended tuning fork (DETF) comprising:

• a pair of spaced apart vibrating beams, generally parallel and joined together at opposing ends, each beam having a thickness t, width w, length m, said DETF having a length L wherein the dimensions for t, w, m and L are selected using a finite element model to satisfy the following relationship:
• ##EQU35## where K.sub.f/fp3 (A,B).noteq.1;
• A=t/w;
• B=L/m and S is the sensitivity of the DETF over a predetermined operating range and the coefficient K(A,B) is selected using a polynomial curve fitting technique to fit the following equation over a predetermined dimensional range:
• K.sub.f/fmn =b.sub.0 +b.sub.1 *B+b.sub.2 *B.sup.2 +b.sub.3 *B.sup.3 +a.sub.1 *A
• where K.sub.f/fmn are the fundamental to spurious mode ratios and the coefficients a and b are determined for each K.sub.f/fmn over the predetermined dimensional range.

A double ended tuning fork (DETF) comprising:

• a pair of spaced apart vibrating beams, generally parallel and joined together at opposing ends, each beam having a thickness t, width w, length m, said DETF having a length L wherein the dimensions for t, w, m and L are selected using a finite element model to satisfy the following relationship:
• ##EQU36## where K.sub.f/fd (A,B).noteq.1;
• A=t/w;
• B=L/m and S is the sensitivity of the DETF over a predetermined operating range and the coefficient K(A,B) is selected using a polynomial curve fitting technique to fit the following equation over a predetermined dimensional range:
• K.sub.f/fmn =b.sub.0 +b.sub.1 *B+b.sub.2 *B.sup.2 +b.sub.3 *B.sup.3 +a.sub.1 *A
• where K.sub.f/fmn are the fundamental to spurious mode ratios and the coefficients a and b are determined for each K.sub.f/fmn over the predetermined dimensional range.

A double ended tuning fork (DETF) comprising:

• a pair of spaced apart vibrating beams, generally parallel and joined together at opposing ends, each beam having a thickness t, width w, length m, said DETF having a length L wherein the dimensions for t, w, m and L are selected using a finite element model to satisfy the following relationship:
• ##EQU37## where K.sub.f/f2d (A,B).noteq.1;
• A=t/w;
• B=L/m and S is the sensitivity of the DETF over a predetermined operating range and the coefficient K(A,B) is selected using a polynomial curve fitting technique to fit the following equation over a predetermined dimensional range:
• K.sub.f/fmn =b.sub.0 +b.sub.1 *B+b.sub.2 *B.sup.2 +b.sub.3 *B.sup.3 +a.sub.1 *A
• where K.sub.f/fmn are the fundamental to spurious mode ratios and the coefficients a and b are determined for each K.sub.f/fmn over the predetermined dimensional range.

A double ended tuning fork (DETF) comprising:

• a pair of spaced apart vibrating beams, generally parallel and joined together at opposing ends, each beam having a thickness t, width w, length m, said DETF having a length L wherein the dimensions for t, w, m and L are selected using a finite element model to satisfy the following relationship:
• ##EQU38## where A=t/w;
• B=L/m and S is the sensitivity of the DETF over a predetermined operating range and the coefficient K(A,B) is selected to fit the following equation over a predetermined dimensional range:
• K.sub.f/fmn =b.sub.0 +b.sub.1 *B+b.sub.2 *B.sup.2 +b.sub.3 *B.sup.3 +a.sub.1 *A
• where K.sub.f/fmn are the fundamental to spurious mode ratios and the coefficients a and b are determined for each K.sub.f/fmn over the predetermined dimensional range.

A double ended tuning fork (DETF) comprising:

• a pair of spaced apart vibrating beams, generally parallel and joined together at opposing ends, each beam having a thickness t, width w, length m, said DETF having a length L wherein the dimensions for t, w, m and L are selected using a finite element model to satisfy the following relationship:
• ##EQU39## where A=t/w;
• B=L/m and S is the sensitivity of the DETF over a predetermined operating range and the coefficient K(A,B) is selected to fit the following equation over a predetermined dimensional range:
• K.sub.f/fmn =b.sub.0 +b.sub.1 *B+b.sub.2 *B.sup.2 +b.sub.3 *B.sup.3 +a.sub.1 *A
• where K.sub.f/fmn are the fundamental to spurious mode ratios and the coefficients a and b are determined for each K.sub.f/fmn over the predetermined dimensional range.

A double ended tuning fork (DETF) comprising:

• a pair of spaced apart vibrating beams, generally parallel and joined together at opposing ends, each beam having a thickness t, width w, length m, said DETF having a length L wherein the dimensions for t, w, m and L are selected using a finite element model to satisfy the following relationships:
• ##EQU40## where K.sub.f/fp (A,B);
• 2K.sub.f/fp1 (A,B);
• K.sub.f/fp2 (A,B);
• 2K.sub.f/fp2 (A,B);
• K.sub.f/fp3 (A,B);
• K.sub.f/fp3 (A,B);
• K.sub.f/fd (A,B) and K.sub.f/f2d .noteq.1.

A double ended tuning fork (DETF) comprising:

• a pair of spaced apart vibrating beams, generally parallel and joined together at opposing ends, each beam having a thickness t, width w, length m, said DETF having a length L wherein the dimensions for t, w, m and L are selected using a finite element model to satisfy the following relationships:
• ##EQU41## where A=t/w;
• B=L/m and S is the sensitivity of the DETF over a predetermined operating range and the coefficient K(A,B) is selected to fit the following equation over a predetermined dimensional range:
• K.sub.f/fmn =b.sub.0 +b.sub.1 *B+b.sub.2 *B.sup.2 +b.sub.3 *B.sup.3 +a.sub.1 *A
• where K.sub.f/fmn are the fundamental to spurious mode ratios and the coefficients a and b are determined for each K.sub.f/fmn over the predetermined dimensional range.