Abstract:
A Coriolis flowmeter that uses a balance bar to allow stress in the active and inactive portions of the flow tube to be as low as possible for any thermal condition. The balance bar has a middle segment that is compliant in the axial direction so that changes in length of the balance bar ends do not impose a significant axial force on the flow lube. This ensures that the thermal stresses on the active and inactive portions of the flow tube are always equal. This state of stress equality is the lowest possible stress state for the flow lube. As a result of the axially compliant balance bar, the remaining stress in the flow tube is only a function of the differential expansion between the flow tube and the case. Balance bar expansion and contraction is eliminated and has no impact on the flow tube stress.

Description:
FIELD OF THE INVENTION 
     This invention relates to a Coriolis flowmeter having a balance bar that can be subjected to a wide range of thermal conditions without applying stresses to the flow tube to which the balance bar is coupled. 
     PROBLEM 
     Single straight tube Coriolis flowmeters traditionally have a concentric balance bar that is coaxial with the flow tube. The balance bar vibrates 180 degrees out of phase with respect to the flow tube to counterbalance the drive mode vibration of the flow tube. The balance bar and the material filled flow tube comprise a dynamically balanced structure that vibrates at its resonant frequency. The ends of the balance bar are rigidly affixed to the flow tube via annular brace bars. Regions of no vibration, called nodes, are located in the brace bars and define the ends of the active portion of the flow tube. 
     The radial distance between the outer surface of the flow tube and the inner surface of the balance bar is traditionally kept small both for reasons of compactness and for tuning the resonant frequency of the balance bar. The small difference in diameter between the flow tube and the balance bar results in a connection that is very rigid. 
     A problem with prior art designs of balance bars is that they impose a significant thermal stress on the flow tube. There are three distinct types of thermal stress of a Coriolis flowmeter. The first is thermal shock. If a Coriolis flowmeter in a cold climate suddenly receives a hot material, the hot flow tube attempts to expand, but is restrained by the surrounding cold balance bar and flowmeter case. Prior art designs use a titanium flow tube having a low modulus of elasticity. The low thermal expansion rate and the high yield strength of titanium enable the flow tube to bear the high stress of thermal shock without damage. 
     The second type of thermal stress is that due to an elevated or lowered uniform temperature of the Coriolis flowmeter. This thermal stress is common in chemical or food plants where Coriolis flowmeter cases are insulated or heated so as to maintain the entire meter at the material temperature. If the entire Coriolis flowmeter were titanium, a uniform meter temperature would not result in any thermal stresses, but titanium is too expensive to use for the entire meter. Most prior art Coriolis flowmeters have a titanium flow tube because of its low expansion and low modulus of elasticity. For cost reasons they have a stainless steel balance bar and case even though titanium would be the preferred material. Thermal stress is produced in these Coriolis flowmeters at elevated uniform temperatures because these different materials have different moduli of expansion. A Coriolis flowmeter that is stress free at 70 degrees has significant stresses at a uniform 200 degrees because the stainless steel balance bar and case expand at more than twice the rate of the titanium flow tube. 
     In the third type of thermal loading, stress is imposed on the flow tube by a steady state thermal condition in which the material and the environment have different temperatures. A Coriolis flowmeter measuring hot material in a cold climate eventually reaches a state of thermal equilibrium in which the titanium flow tube reaches the material temperature while the balance bar is only slightly cooler. The case, however, can be much cooler depending on the ambient conditions. If the case is exposed to a cold wind, for example, the case temperature may be only a few degrees above the ambient temperature. Stresses are generated when the cool case restrains attempted expansion by the balance bar and the flow tube. Stresses are also generated when the stainless steel balance bar attempts to expand at twice the rate of the titanium flow tube. 
     Commercially available single straight tube flow Coriolis flowmeters must be able to withstand all three types of thermal loading without suffering permanent damage and ideally without excessive error in the material measurement. The balance bar ends are rigidly affixed to the flow tube via brace bars. This effectively divides the flow tube into three portions. The central portion, between the brace bars and within the balance bar is the active portion of the flow tube. This portion vibrates out of phase with respect to the balance bar. The two portions of the flow tube that extend from the ends of the balance bar to the case ends do not vibrate and are the inactive portions of the flow tube. 
     When the above described prior art Coriolis flowmeter is exposed to the first type of thermal loading, thermal shock, both the active and inactive portions of the flow tube experience the same thermal stress. This is due to the fact that neither the balance bar, which constrains the active portion of the flow tube, nor the case, which constrains the inactive portions of the flow tube change temperature or length and the three portions of the flow tube quickly attain the same elevated temperature as the material and have the same thermal stress. When the prior art Coriolis flowmeter is exposed to the second type of thermal loading in having a uniform elevated temperature, the three portions of the flow tube once again experience the same thermal stress. The balance bar and case are both stainless steel and expand at the same rate. The titanium flow tube, attempts to expand at a different rate but is restrained by the balance bar and case. 
     Under the third thermal condition of thermal loading, the flow tube and the balance bar nearly attain the material temperature while the case remains cold. The hot balance bar expands its length while the cold case does not. The inactive flow tube portions are between the case ends and the lengthening balance bar. The balance bar and case both have much larger cross section areas than the flow tube and force the inactive portions of the flow tube to decrease in length. Since the inactive flow tube portions are hot and if unconstrained would be increasing in length, the forced decrease in length results in stress that can even exceed the yield strength of the titanium flow tube. Meanwhile, the active portion of the flow tube is constrained at its ends by the connections to the hot stainless steel balance bar. Stainless steel has a much greater expansion coefficient than the titanium of the flow tube. Depending on the temperature differential between the balance bar and the flow tube, the active portion of the flow tube could be put in tension since the balance bar temperature is nearly equal to the flow tube temperature. It could also be put in compression as when the balance bar temperature is lower than the flow tube temperature. 
     The situation in which the inactive portion of the flow tube is highly stressed by temperature gradients is a problem with prior art flow Coriolis flowmeters. The problem is generally solved in prior art Coriolis flowmeters by limiting the temperature range over which the Coriolis flowmeters may be operated. This is undesirable since many customers would like to measure material flow rate at temperatures that exceed the limits dictated by thermal stress. 
     SOLUTION 
     The present invention overcomes the above and other problems by use of a balance bar that allows the stresses in the active and inactive portions of the flow tube to be as low as possible for any thermal condition. The balance bar has a middle segment that is compliant in the axial direction so that changes in length of the balance bar ends do not impose a significant axial force on the flow tube. This ensures that the thermal stresses on the active and inactive portions of the flow tube are always equal. This state of stress equality is the lowest possible stress state for the flow tube. As a result of the axially compliant balance bar, the remaining stress in the flow tube is only a function of the differential expansion between the flow tube and the case. Balance bar expansion and contraction is eliminated and has no impact on the flow tube stress. 
     A further advantage of the balance bar of the present invention is cost. Most prior art Coriolis flowmeters require a stainless steel balance bar to keep the cost reasonable. In order to extend the temperature range of a Coriolis flowmeter, the balance bar of the prior art is required to have an expansion coefficient as near as possible to that of the flow tube material (titanium). The best balance bar of the prior art would be one made entirely of titanium. However, the cost of a titanium balance bar in larger sized Coriolis flowmeters can be as much as six times that of a stainless steel balance bar. The balance bar of the present invention has an increased axial compliance that does not impose axial forces on the flow tube. The balance bars thermal expansion is of no concern and thus can be made of less expensive material and have a wide temperature range. 
     There are several possible exemplary embodiments of the present invention. A first embodiment is a balance bar having two independent end portions and a void for a center portion. Each end portion is fastened to a respective brace bar and, via the brace bars, to the ends of the active portion of the flow tube. The independent balance bar end portions behave as cantilever beams that are designed to have the resonant frequency of the material filled flow tube. The void enables the lowering of the balance bar drive mode frequency to that of the flow tube without the added balance bar mass of prior art meters. It does this by removing stiffness from the balance bar. This dynamically balances the Coriolis flowmeter. The driver comprises a drive coil that is fastened to the case because of the void in the central portion of the balance bar, and a magnet fastened to the flow tube. The independent balance bar end portions are passively driven by the motion of the brace bars in response to the drive mode vibration of the flow tube. The independent balance bar end portions respond to the drive mode vibration of the flow tube and apply a torque to the brace bar regions that counters the torque applied to the brace bars by the ends of the active portion of the flow tube. The deflection of the balance bar end portions also counter the momentum of the vibrating flow tube. 
     This balance bar design has an added benefit beyond reduced cost and extended temperature range with no resulting stress on the flow tube. A balance bar in prior art single tube flowmeters has been able to counterbalance the vibration of the flow tube in the drive mode, but it does not balance the vibration of the flowmeter caused by the Coriolis forces applied to flow tube during conditions of material flow. Coriolis forces and deflections are applied to a vibrating flow tube with material flow. The two axial halves of the flow tube have applied Coriolis forces of opposite directions. The resulting Coriolis deflections of the two axial halves of the flow tube are also in opposite directions. These forces and deflections are proportional to the material flow rate and they generate vibrations that cannot be counterbalanced by fixed weights on a traditional balance bar. 
     The balance bar of the present invention is able to counterbalances these Coriolis forces because of the independence of its two end portions. The void in the center of the balance bar lowers the resonant frequency of the balance bar end portions in a mode in which they vibrate out of phase with each other. This mode is referred to as the Coriolis-like mode because of its shape. The void lowers the resonant frequency of this mode to below the drive frequency. Each balance bar end portion resonates out of phase with the flow tube in the drive mode frequency of vibration. Because Coriolis deflections of the flow tube occur at the drive mode frequency, the two independent balance bar end portions respond to these Coriolis deflections as readily as to the drive mode deflections. The driving force for these two responses is the same. It is the motion of the brace bars. The left balance bar end portion has the same response to the Coriolis excitation as it does for the drive mode excitation. The difference between the two excitation modes is that the drive mode excitation is of a constant amplitude and the two ends of the active of the flow tube are in phase with each other. The Coriolis excitation has an amplitude that is proportional to the flow rate and the two ends of the active portion of the flow tube are 180 degrees out of phase with each other. The independent balance bar end portions have Coriolis-like deflections that effectively counterbalance the Coriolis forces of the flow tube. The out-of-phase Coriolis-like deflections increase the amplitude of vibrations of the balance bar and are out of phase with the Coriolis vibrations of the flow tube as the flow rate (and thus the Coriolis force) increases. 
     The counterbalancing of the Coriolis force vibrations by the balance bar end portions produces a more accurate Coriolis flowmeter. The unbalanced Coriolis forces of prior art Coriolis flowmeters result in a shaking of the Coriolis flowmeter at the drive mode frequency. This shaking, which is proportional to flow rate alters the Coriolis acceleration of the material flow and the resultant output signals of the pick offs. Compensation could be made for this error except that it is dependent upon Coriolis flowmeter mounting stiffness. A Coriolis flowmeter with rigid mount would have a slight error while a Coriolis flowmeter with a soft mount would have greater error. Since the mounting conditions of a Coriolis flowmeter in commercial use are unknown, it is generally not possible to compensate for them. 
     An alternative embodiment of the invention has balance bar end portions that are weakly coupled by drive coil brackets. These brackets allow the driver to be mounted in the axial center so that the coil and magnet of the driver can drive the balance bar end portions and flow tube in phase opposition. These brackets are made of sufficiently thin metal and their geometry is such that they allow the balance bar end portions to expand and contract axially with little resistance. 
     These flexible brackets also allow for the out of phase motion of the two balance bar end portions that counterbalance the applied Coriolis forces. 
     Another alternative embodiment allows for expansion and contraction of the two balance bar end portions, but does not allow for an out of phase motion of the two end portions. This permits the use of an inexpensive balance bar material along and provides a high temperature range. This embodiment does not allow for the out of phase motion of the balance bar end portions that counterbalances the Coriolis forces. 
     Yet another embodiment provides a balance bar with independent end portions coupled to a center section by flexible side strips. Cutouts in the center section and balance bar halves increase axial compliance. 
     In summary, the present invention solves three balance bar problems by decoupling the two end portions of the balance bar. It allows the balance bar to be made of less expensive materials. It allows for a wider temperature range with less axial stress on the flow tube and it provides a more accurate Coriolis flowmeter by counterbalancing the Coriolis forces applied to the flow tube. 
     An aspect of the invention is a Coriolis flowmeter adapted to receive a material flow at an inlet and to extend said material flow through flow tube means to an outlet of said Coriolis flowmeter; said Coriolis flowmeter also includes: 
     a balance bar positioned parallel to said flow tube means; 
     brace bars coupling ends of said balance bar to said flow tube means; 
     a driver that vibrates said flow tube and balance bar in phase opposition; 
     pick off means coupled to said balance bar and to said flow tube means to generate signals representing the Coriolis response of said vibrating flow tube means with material flow; 
     a first end portion of said balance bar extending axially inward from a first one of said brace bars towards a mid-portion of said balance bar; 
     a second end portion of said balance bar extending axially inward from a second one of said brace bars towards said mid-portion of said balance bar; and 
     an axial mid-portion of said balance bar having a compliance that enables said balance bar to expand and contract axially without imparting any axial stress to said flow tube. 
     Another aspect is that said mid-potion of said balance bar is a void. 
     Another aspect is that said flow tube means comprises a straight flow tube. 
     Another aspect is that said driver is positioned proximate said mid-portion and is coupled to an exterior surface of said flow tube and an inner wall of said case. 
     Another aspect is that a magnet of said driver is affixed to said exterior surface of said flow tube and a coil of said driver is coupled to said inner wall of said case. 
     Another aspect is a Coriolis flowmeter adapted to receive a material flow at an inlet and to extend said material flow through flow tube means to an outlet of said Coriolis flowmeter; said Coriolis flowmeter also includes: 
     a balance bar positioned parallel to said flow tube means; 
     brace bars coupling ends of said balance bar to said flow tube means; 
     a driver that vibrates said flow tube and balance bar in phase opposition; 
     pick off means coupled to said balance bar and to said flow tube means to generate signals representing the Coriolis response of said vibrating flow tube means with material flow; 
     a first end portion of said balance bar extending axially inward from a first one of said brace bars towards a mid-portion of said balance bar; 
     a second end portion of said balance bar extending axially inward from a second one of said brace bars towards said mid-portion of said balance bar; 
     an axial mid-portion of said balance bar; 
     said mid-portion comprises: 
     drive coil bracket means; 
     spring means oriented substantially perpendicular to the longitudinal axis of said flow tube and coupling said drive coil bracket means to the axial inner extremities of said end portions of said balance bar, said spring means having an axial compliance that enables said end portions of said balance bar to change in length without imparting any axial stress to said flow tube exclusive of the stress associated with the force required to flex said spring means as said length of said end portions change. 
     Another aspect is that said spring means flex as the axial length of said end portions of said balance bar changes with the only resultant axial stress imparted to said flow tube being the stress required to flex said springs means. 
     Another aspect is that said flow tube means comprises a single straight flow tube. 
     Another aspect is that said balance bar is co-axial with said flow tube. 
     Another aspect is that said pick off means comprises a pair of velocity sensors with a first one of said pick offs being coupled to said first end portion of said balance bar and to said flow tube and with a second one of said pick offs being coupled to said second end portion of said balance bar and said flow tube. 
     Another aspect comprises a case enclosing said flow tube and said brace bars and said balance bar. 
     Another aspect is that: 
     said material flow through said vibrating flow tube imparts Coriolis deflections to said flow tube; 
     said material flow through said vibrating flow tube imparts Coriolis-like deflections to said first and second end portions of said balance bar that are in phase opposition to said Coriolis deflections of said flow tube. 
     Another aspect is that said first and second end portions of said balance bar vibrate independently in phase with each other for drive mode vibrations imparted to said flow tube by said driver. 
     Another aspect is that said first and second end portions of said balance bar vibrate out of phase with each other for said Coriolis-like deflections imparted to said balance bar by said Coriolis deflections of said flow tube. 
     Another aspect is that a first end of said spring means is coupled to said drive coil bracket means; 
     a second end of said spring means is coupled to the axial inner extremity of said end portions of said balance bar; 
     said spring means flexes in response to said axial changes in length of said end portions of said balance bar. 
     Another aspect is that said drive coil bracket means comprises: 
     a drive coil bracket having a flat surface parallel to a longitudinal axis of said flow tube; 
     a second bracket having a surface parallel to said longitudinal axis of said flow tube; 
     said spring means comprises a first set of springs coupling said first drive coil bracket to said axial inner extremities of said end portions of said balance bar; 
     said flat surface of said first drive coil bracket is adapted to receive a coil of said driver; 
     a drive magnet is coupled to said flow tube and in magnetic communication with said drive coil; 
     said spring means further comprising a second set of springs coupling said second said drive coil bracket to said axial a inner extremities of said end portions of said balance bar; and 
     a mass affixed to said flat surface of said second bracket. 
     Another aspect is that said springs of said first and second set have ends coupled to said inner axial extremities of said balance bar end portions. 
     Another aspect is that: 
     said drive coil bracket means is coaxial with said flow tube and has an axial length less than the distance between said axial inner extremities of said balance bar end portions; 
     elongated support bars couple said axial inner extremities of said balance bar end portions to the axial outer extremities of said drive coil bracket means; 
     said elongated support bars are positioned in a vibrationally neutral plane of said balance bar and are oriented parallel to said longitudinal axis of said flow tube; 
     slots are in the walls of said drive coil bracket means, said slots are parallel to and proximate said outer axial extremities of said drive coil bracket means; 
     the wall material of said drive coil bracket means between said slots; and said outer axial extremities of said drive coil bracket means define a first set of springs that flex in response to changes in the axial length of said balance bar end potions; 
     Another aspect is that: 
     circumferentially oriented slots are in the walls of said balance bar end portion proximate said axial inner extremities of said balance bar end portions; 
     the wall material between said slots and said balance bar end portions; and define a second set of springs that flex axially in response to changes in the axial length of said balance bar end potions and in response to changes in the length of said flow tube. 
     Another aspect is that: 
     said support bar and set first and second set of springs define springs that flex in response to changes in the axial length of said balance bar end potions without imparting axial stress to said flow tube in excess of the stress associated with the force required to flex said first and second set of springs and said support bar. 
     Another aspect is that: 
     a top portion of said drive coil bracket has a flat surface with an opening for receiving a coil of said driver; 
     a magnet of said driver is in electromagnet communication with said drive coil and is coupled to said flow tube. 
     Another aspect is that: 
     said drive coil bracket means is cylindrical and has a diameter substantially equal to the diameter of said balance bar. 
     Another aspect is that said drive coil bracket means comprises: 
     a first drive coil bracket affixed to a top portion of said first balance bar end portion proximate said inner axial extremity of said first end portion; 
     a second drive coil bracket affixed to a bottom portion of said second balance bar end portion proximate said inner axial extremity of said second end portion; 
     spring means oriented substantially perpendicular to said longitudinal axis of said flow tube that couples said first drive coil bracket to said second drive coil bracket; 
     said spring means is adapted to flex about its end in response to changes in the axial length of said end portions of said balance bar; 
     said spring means having a flexibility that enables said end portions of said balance bar to change in length to change in length without imparting a stress to said flow tube in excess of a stress associated with the force required to flex said springs. 
     Another aspect is that said spring means comprises: 
     a first end of said spring means coupled to said first drive coil bracket; 
     a second end of said spring means coupled to said second drive coil bracket. 
     Another aspect includes a first mass affixed to a lower portion of said inner axial extremity of first end potion of said balance bar; 
     a second mass affixed to an upper portion of said inner axial extremity of said second end potion of said balance bar. 
     Another aspect is that said driver comprises: 
     a first drive coil affixed to a surface of said first drive coil bracket; 
     a first magnet in magnetic communication with said first drive coil and affixed to said flow tube; 
     a second drive coil affixed to a surface of said second drive coil bracket; 
     a second magnet in magnetic communication with said second drive coil and affixed to said flow tube; 
     said drive coils being and said magnets being effective in response to the receipt of a drive signal coils for vibrating said flow tube and said balance bar in phase opposition. 
    
    
     DESCRIPTION OF THE DRAWINGS 
     The invention may be better understood from a reading of the following detailed description thereof taken in conjunction with the drawings in which: 
     FIG. 1 discloses a prior art straight tube Coriolis flowmeter. 
     FIG. 2 discloses a straight Coriolis flowmeter in accordance with a first exemplary embodiment of the invention. 
     FIGS. 3,  4 , and  5  disclose mode shapes of the flow tube and balance bar in accordance with the present invention. 
     FIGS. 6 and 7 disclose a straight tube Coriolis flowmeter in accordance with a second exemplary embodiment of the invention. 
     FIGS. 8 and 9 disclose a straight tube Coriolis flowmeter in accordance with a third exemplary embodiment of the invention. 
     FIGS. 10,  11 , and  12  disclose a straight tube Coriolis flowmeter in accordance with a fourth exemplary embodiment of the invention. 
    
    
     DETAILED DESCRIPTION 
     Description of FIG. 1 
     FIG. 1 discloses a straight tube Coriolis flowmeter  100  having a straight flow tube  101  surrounded by balance bar  102  with flow tube  101  and balance bar  102  being surrounded by case  104 . Brace bars  110  and  111  couple end portions of balance bar  102  to the outer walls of flow tube  101 . Flow tube  101  also includes flow tube extension elements  101 A and  101 B. Element  101  is the active portion of the flow tube between brace bars  110  and  111 . Extension elements  101 A and  101  B are the inactive portions of the flow tube and connect brace bars  110  and  111  to case ends  108  and  109 . Elements  113  and  114  may be considered to be a portion of the flow tube and since these elements extend through neck  105  and  115  to flanges  112  and  112 A. Element  106  is the material input of the flowmeter. Element  107  is the material output of the flowmeter. Meter electronics  121  applies a signal over path  123  to Driver D to vibrate balance bar  102  and flow tube  101  in phase opposition. Pick offs (velocity sensors) LPO and RPO detect the vibrations of the flow tube  101  with material flow and generate output signals indicating phase of the Coriolis response. The pick off and output signals are applied over paths  122  and  124  to meter electronics  121  which generates an output on path  125  containing information regarding the material flow. 
     Balance bar  102  is rigidly coupled to flow tube  101  by brace bars  110  and  111 . Flow tube  101  is tightly coupled to case ends  108  and  109  by flow tube portions  101 A and  101 B. This tight coupling of the flow tube to the balance bar and to the case creates thermal stresses on the flow tube during conditions in which the flow tube temperatures suddenly increases with respect to the balance bar  102  and case  104  as well as steady state conditions in which the flow tube temperature differs from that of balance bar  102  and/or case  104 . 
     There are three possible types of thermal stress within a Coriolis flowmeter. The first type is thermal shock. In this, the flow tube  101  may suddenly receive a hot (or cold) material. The hot flow tube  101  attempts to expand, but is restrained by the surrounding cold balance bar  102  and case  104 . This stress generated under this condition results in the active portion  101  of the flow tube attempting to expand axially more than the cold balance bar. Inactive flow tube portions  101 A and  101  B are subject to this stress and attempt to expand axially more than does case  104 . Problems resulting from the thermal stress are minimized if the flow tube is made of titanium because of the low modulus of elasticity of titanium. Although the use of a titanium flow tube minimizes the stress problems, the stress on the flow tube can alter the rigidity of the flow. This degrades the accuracy of the output information generated by the vibrating flow tube and, in turn, the Coriolis flowmeter. 
     A second type of thermal stress occurs when the entirety of the flowmeter is subject to an elevated or lowered uniform temperature. Even with the use of a titanium flow tube, the flow tube experiences thermal stress since the stainless balance bar  102  and case  104  attempt to expand it more than twice the rate of the titanium flow tube  101 . Even if the titanium flow tube is able to withstand this stress without permanent mechanical deformation, its altered stiffness degrades the accuracy of the output information generated. 
     A third type of thermal stress is characterized by a steady state thermal condition in which the flowing material and the environment have different temperatures. A Coriolis flowmeter measuring hot material in a cold climate eventually achieves a state of thermal equilibrium in which the titanium flow tube reaches the material temperature with the balance bar being only slightly cooler. The case can be much cooler, depending upon ambient conditions, such as use in the Arctic. Stresses are generated when the cool case restrains attempted expansion by the balance bar and the flow tube. Stresses-are also generated when the stainless steel balance bar attempts to expand at twice the rate of the titanium flow tube. Under these conditions, the hot balance bar attempts to expand in length while the cold case does not. The inactive portions of the flow tube  101 A and  101 B are connected between the case ends and the expanding balance bar. The balance bar and case both have much larger cross sections then the flow tube and they force the inactive portions  101 A and  101 B of the flow tube to decrease in length. Since these inactive flow tube portions are attempting to increase in length, the force applied by the larger balance bar stresses flow tube portions  101 A and  101 B. The stress levels can exceed the yield strength of a titanium flow tube. Meanwhile, the active portion  101  of the flow tube is constrained at its ends by the balance bar and the brace bars. The stainless steel balance bar has a much greater coefficient of expansion than the titanium flow tube. Thus, depending upon the temperature differentials between the stainless steel balance bar and the titanium flow tube, the active portion of the flow tube  101  could be put in tension. It also could be put in compression when the balance bar temperature is lower than the flow tube temperature. 
     It can therefore been seen that it is a problem that a straight tube prior art Coriolis flowmeter as shown in FIG. 1 suffers from thermal stresses on the flow tube that adversely degrade the accuracy of the output information generated by the flowmeter and in extreme cases can further permanently damage the flow tube. 
     Description of FIG. 2 
     FIG. 2 discloses a first possible exemplary embodiment of the invention comprising a straight tube Coriolis flowmeter  200  that is similar in many respects to prior art Coriolis flowmeter  100  of FIG.  1 . The difference is that the center section of the balance bar of FIG. 2 has been removed. 
     FIG. 2 discloses a straight tube Coriolis flowmeter  200  having a flow tube having active portion  201  and inactive portions  201 A and  201 B. Coriolis flowmeter  200  further includes balance bar end segments  202 ,  203  and a void center segment  202 V, a case  204  and end flanges  212  and  212 A. Case  204  has end portions  208  and  209  connected by necks  205  and  215  to end flanges  212  and  212 A. The inlet of the flowmeter is element  206  on the left; the outlet is element  207  on the right. Cone connect links  213  and  214  couple the inner wall of the necks  205  and  215  to the exterior surface of flow tube elements  201 A and  201 B. Brace bars  210  and  211  couple the outer axial end portions of brace bar segments  202  and  203  to flow tube  201 . Pick offs LPO and RPO each comprise a coil C and a magnet M. Driver D comprises a magnet  217  affixed to flow tube  201  and coil  216  connected to a flat surface of drive coil bracket  221  whole leg portions are connected to the inner wall  220  of case  204 . Element  222  is the axially inner end of balance bar segment  202 ; element  223  is the axially inner end of balance bar segment  203 . 
     In the same manner as described for FIG. 1, driver D causes the flow tube  201  and the brace bar segments  202  and  203  to vibrate in phase opposition. The vibration of flow tube  101  extends vibratory forces through brace bars  110  and  111  to the end portions of balance bar end segment  102  and  103  to cause them to vibrate in phase opposition to the flow tube  101  with respect to drive mode vibrations of the flow tube. Pick offs (velocity sensors) LPO and RPO detect the Coriolis response of vibrating flow tube  201  with material flow and generate output signals indicative of the material flow. These output signals are extended over paths  122  and  124  to meter electronics  121  which processes the signals and generates output information indicative of the material flow. 
     Since Coriolis flowmeter  200  of FIG. 2 has a void  202 V for the center portion of its balance bar, the two independent balance bar end segments  202  and  203  are fastened to the respective brace bars  210  and  211  and, via the brace bars, to the active portion  201  of the flow tube. The balance bar end segments  202  and  203  behave as cantilever beams and each has the same resonant frequency as the material filled vibrating flow tube. Since the flow tube and the balance bar end segments  202  and  203  are vibrated in phase opposition, and since they have the same resonant frequency, they constitute a dynamically balanced vibratory structure that imparts no vibration external to the flowmeter. / 
     Description of FIGS. 3,  4 , and  5   
     FIG. 3 shows how the independent balance bar segments  202  and  203  of FIG. 2 respond to the drive mode vibration of flow tube  201 . This drive mode vibration generates torques which are applied by the flow tube to brace bars  210  and  211 . This torque is extended to end segments  202  and  203  of the balance bar to cause them to vibrate in phase opposition to their corresponding portion of flow tube  201 . This deflection of the balance bar end segments counters that of the vibrating flow tube so that the flow tube and the balance bar end segments together cancel the vibration and torque of one another and generate a dynamically balanced vibrating structure. This balance bar has the added benefits that it reduces the costs of the materials used in the balance bar and provides a lower stress on the flow tube over an extended temperature range. 
     The balance bar of the Coriolis flowmeter of FIG. 1 counter-balances the vibration of the flow tube in the drive mode, but it does nothing to balance the vibration of the flowmeter caused by the Coriolis forces applied to the flow tube during material flow. FIG. 4 illustrates the Coriolis forces and resultant deflections on a vibrating flow tube  201  with material flow. The arrows illustrate that the Coriolis forces applied to the two halves of the active flow tube  201  are in opposite directions. On FIG. 4, the Coriolis force arrows on the left half of the flow tube are in an upward direction; those on the right half are in a downward direction. As a result, the resultant Coriolis deflections on the two halves of the flow tube are in opposite directions. These forces and deflections are proportional to the magnitude of the material flow rate and cannot be counter balanced by affixing weights to the balance bar. Also, the forces applied to the flow tube continuously vary in magnitude and direction sinusoidally at the drive mode frequency. For the conditions shown in FIG. 4, it can be seen that flow tube  201  attempts to rotate clockwise about its center C because the upward forces are applied to its left half  303  and downward forces are applied to its right half  304 . Later in the vibratory cycle, these forces change direction and the flow tube then attempts to rotate about its center C in a counterclockwise direction. This oscillatory change of rotational forces on the flow tube creates undesired vibrations, which can adversely affect the output accuracy of the material flow information generated by the flowmeter. 
     Since the Coriolis deflections of FIG. 3 occur at the drive mode frequency, it follows that the balance bar end segments respond to these Coriolis deflections of the flow tube as readily as it does to the drive mode deflections of the flow tube. The driving force for these two responses is the same. It is the vibratory motion of brace bars  210  and  211 . This is shown in FIG.  5 . It can be seen that the left balance bar segment  202  has the same response to the same excitation as the left balance bar half of FIG.  3 . The difference between the two excitation modes is that the drive excitation is a constant amplitude and the ends of the active portion of flow tube  201  are in phase with each other. The Coriolis excitation mode has amplitude that is proportional to the material flow rate and the vibrations of the two end segments  202  and  203  of the balance bar are 180° out of phase with each other. The balance bar end segments  202  and  203  effectively counter balance the Coriolis forces on the flow tube because they increase their amplitude of vibration as the flow rate and the Coriolis force increases. It can be seen in FIG. 5 that the deflections of balance bar end segments  202  and  203  are out of phase with the Coriolis deflections of their corresponding portions of flow tube  201 . As a result, the Coriolis forces applied to the vibrating flow tube with material flow are effectively counter balanced by the off setting vibratory deflections of their corresponding portions of balance bar end segments  202  and  203 . This counter balancing of the Coriolis forces produces a more accurate Coriolis flowmeter since the unbalanced Coriolis forces of the prior art Coriolis flowmeters that result in a shaking of the Coriolis flowmeter at the drive frequency are eliminated in the Coriolis flowmeter of the present invention. 
     Description of FIGS. 6 and 7 
     FIGS. 6 and 7 disclose an alternative embodiment of a Coriolis flowmeter  600  embodying the present invention. This embodiment differs from that of FIG. 2 primarily in the fact that the two balance bar end segments  602  and  603  are coupled by a center section comprising a flexible drive coil bracket  640 . This bracket  640  allows a coil of driver D to be mounted in the traditional location as part of the balance bar. The driver coil and an associated magnet on the flow tube can directly drive the balance bar end sections in phase opposition to the flow tube  601 . The drive coil bracket  640  structure includes leaf-springs  638  which are flexible and which allow the balance bar end sections to expand and contract axially with no resulting stress on the flow tube beyond those associated with the force required to flex leaf-springs  638 . Leaf-springs  638  also allow the balance bar end segments  602  and  603  to assume a Coriolis-like response that is out of phase to the Coriolis response of the flow tube and which counter balances the Coriolis deflections of the vibrating flow tube. 
     Drive coil bracket structure  640  includes a flat surface  646  on which driver coil  644  is mounted. This structure  640  includes four leaf-springs  638  which have a right angle bend at their lower extremity and are affixed to support bar  642  which comprise extensions of the inner extremities  636 ,  637  of balance bar end segments  602  and  603 . Element  640 A is a bracket having an opening  641  that mounts mass  643 . Bracket  640 A is coupled to support bars  642  by a lower set of springs  638 A. Mass  643  dynamically balances the mass of drive coil  644 . The rest of the flowmeter structure of the embodiment of FIGS. 6 and 7 is analogous to that of the embodiment of FIG.  2  and comprises the following described elements. Case  604 , case ends  608  and  609 , inlet  606 , necks  605  and  615 , cone connect elements  613  and  614 , and flow tube  601  including its inactive end portions  601 A and  601 B. Case connect links  631  and  632  having out of plane bend element  634 , brace bars  610  and  611  including side wall extensions  610 A and  611 A, inner wall  620  of case  604 , pick offs LPO and RPO as well as driver D, magnet bracket  639 , magnet M mounted on bracket  639 , coil  644 , inner walls  602 A and  603 A of balance bar end segments  602  and  603 , and outlet  607 . These elements all are analogous to and perform the same functions as their counterparts on the embodiment of FIG.  2 . 
     Springs  638  of FIGS. 6 and 7 have thermal expansion capabilities that do not stress the flow tube  601  as the balance bar end segments  602  and  603  change in length. The lengthening or shortening of the balance bar end segments causes the leg springs to bend. This bending produces only small stresses in the leg springs because of their thinness. The only stress on the flow tube is that associated with the small force required to flex springs  638 . This embodiment lowers the resonant frequency of balance bar end segments  602  and  603  in the drive mode to that of the resonant frequency of flow tube  601 . It also lowers the resonant frequency of the Coriolis-like mode of the balance bar to below the drive frequency. The lowered resonant frequency of balance bar end segments  602  and  603  permits them to have a Coriolis-like response that is in phase opposition to the Coriolis deflections of flow tube  601 . This Coriolis-like response of the balance bar end sections enhances the material flow sensitivity of the Coriolis flowmeter of embodiment of FIGS. 6 and 7 and balances the Coriolis forces on the flow tube. 
     In the same manner described for the embodiment of FIG. 1, meter electronics  121  applies a signal over path  123  to Driver D to vibrate balance bar  102  and flow tube  101  in phase opposition. Pick offs LPO and RPO detect the vibrations of the flow tube  101  with material flow and generate output signals indicating the magnitude and phase of the Coriolis response. The pick off and output signals are applied over paths  122  and  124  to meter electronics  121  which generates an output on path  125  containing information regarding the material flow. 
     In summary of the embodiment of FIGS. 6 and 7, flexible drive coil bracket  640  intermediate balance bar end segments  602  and  603  lowers the resonance frequency of segments  602  an  603  in the drive mode to that of flow tube  601 . Flexible drive coil bracket  640  also lowers the resonant frequency of balance bar end segments  602  and  603  in the Coriolis-like deflection mode to below drive frequency. This enhances the Coriolis-like out of phase response of the balance bar end segments  602  and  603  with respect to flow tube  601 . This enhances the material flow sensitivity of the Coriolis flowmeter. However, drive coil bracket  640  must be carefully designed to prevent the generation of unwanted vibrations that could adversely affect the accuracy or the output data of the Coriolis flowmeter. This embodiment is advantageous in that leg-springs  638  easily flex and protect flow tube  601  from axial stress in response to changes in the axial length of balance bar end segments  602  and  603 . 
     Description of FIGS. 8 and 9 
     FIGS. 8 and 9 disclose yet another alternative exemplary embodiment comprising Coriolis flowmeter  800  embodying the invention. This embodiment is similar in many respects to the embodiment of FIGS. 2,  6 , and  7  with the exception of the drive coil bracket structure in the middle of the balance bar between the balance bar end segments  802  and  803 . The embodiment of FIG. 2 has a void  202 V for a center section of the balance bar; the embodiment of FIGS. 6 and 7 has a flexible drive coil bracket  640  for the center section of the balance bar. Flowmeter  800  of FIGS. 8 and 9 has a center drive coil bracket  841  that interconnects the inner axial extremities  836  and  837  of balance bar end segments  802  and  803 . 
     Drive coil bracket  841  has an outer circumferential surface  843 , a flat  838  on its top portion for permitting the mounting of coil  844  of driver D. Drive coil bracket  841  also has slots  842 . Drive coil bracket  841  is connected by support bars  835  to the axial inner extremities  836  and  837  of balance bar end segments  802  and  803 . Balance bar end segment  802  has slot proximate its right end; balance bar end segment  803  has slot  833  proximate it&#39;s left end. Slots  833  of the balance bar end sections and the corresponding slots  842  of drive coil bracket  841  define leg springs  846  that provide an axial compliance that accommodates thermal expansion and contraction of balance bar end segments  802  and  803 . The rear side of the balance bar end segments and the rear side of the drive coil bracket  841  have similar slots that cannot be seen in this view. The compliance provided by leg springs  846  is not as great as that of the preceding two described embodiments. This compliance, however, can significantly lower the stress produced in the flow tube by the expansion and contraction of the balance bar. Slots  832  and  833  also lower the resonant frequency of balance bar end segments  802  and  803  so as to facilitate spring rate balancing of these elements as well, to provide a lower resonant frequency of balance bar ends segments  802  and  803  that permits these elements to have a Coriolis-like response that is in phase opposition to the Coriolis deflections of flow tube  801 . The remainder of the elements comprising the embodiment of FIGS. 8 and 9 is similar to that already described for the embodiments of FIG.  2  and FIGS. 6,  7 . These elements include case  804 , case ends  808  and  809 , neck portions  805  and  815 , inlet  806 , outlet  807 , cone connect elements  813  and  814 , flow tube section  801 A and  801 B, case connect links  831  and  832  having out of plane bends  834  and  834 A, brace bars  810  and  811  together with brace bar side walls extensions  810 A and  81   1 A, pick offs LPO and RPO, driver D, inner wall  820  of case  804 . 
     In the same manner as described for the embodiment of FIG. 1, meter electronics  121  applies a signal over path  123  to Driver D to vibrate balance bar  102  and flow tube  101  in phase opposition. Pick offs LPO and RPO detect the vibrations of the flow tube  101  with material flow and generate output signals indicating the magnitude and phase of the Coriolis response. The pick off and output signals are applied over paths  122  and  124  to meter electronics  121  which generates an output on path  125  containing information regarding the material flow. 
     In summary with respect to the embodiment of FIGS. 8 and 9, the flexible drive coil bracket  841  intermediate balance bar end segments  802  and  803  lowers the resonance frequency in of segments  802  an  803  the drive mode to that of the flow tube. It also lowers the resonant frequency in the Coriolis-like mode to less than the drive frequency. This enhances the Coriolis-like out of phase response of the balance bar end segments  802  and  803  with respect to flow tube  801  and enhances the material flow sensitivity of the Coriolis flowmeter. However, drive coil bracket  841  must be carefully designed to prevent the generation of unwanted vibrations that could adversely affect the accuracy or the output data of the Coriolis flowmeter. This embodiment is advantageous in that the leg-springs  846  defined by the slots  833  and  842  function as springs that flex and protect flow tube  801  from axial stress in response to changes in the axial length of balance bar end segments  802  and  803 . 
     Description of FIGS. 10,  11 , and  12   
     FIGS. 10,  11 , and  12  disclose a Coriolis flowmeter  1000  embodying yet another exemplary embodiment of the invention. This embodiment differs from the previously described embodiments only in the details of the center drive coil bracket  1040  which comprises the center portion of the balance bar whose other two segments are left hand end portion  10002  and right hand end portion  10003 . The drive coil bracket  1040  includes a pair of drivers D 1  and D 2 , mass element  1041  on the right end of balance bar end segment  1002 , mass  1035  on the left end of balance bar end segment  1003 , coil brackets  1042  and  1043 , leaf springs  1045  which interconnect drive coil brackets  1042  and  1043 , driver coils  1044  and  1045  and associated magnets  1202  and  1204 , flow tube bracket  1042  having flat surface  1046  for enabling the mounting of coils  1044  and  1044 A. As shown in detail in FIG. 12, the top surface  1046  of drive coil bracket  1042  has an arcuate cut out  1208  for receiving magnet  1202 . The top ends of leaf springs  1045  are affixed to the right vertical surfaces  1209  of drive coil bracket  1042 . 
     Mass  1035  and drive coil bracket  1043  affixed to balance bar segment  1003  on FIG. 10 not shown on FIG. 12 in order to minimize the complexity of the drawing. However, it is obvious to one skilled in the art that coil  1044  of driver D 2  on FIG. 12 would be affixed to drive coil bracket  1043  and that the lower ends of leaf springs  1045  would be affixed to a left vertical surface of coil drive coil bracket  1043 . 
     Leaf springs  1045  moveably couple the center end portions of balance bar segments  1002  and  1003  to enable them to change in length in response to varying thermal conditions. This change in length of balance bar segments  1002  and  1003  results in a flexing of leaf springs  1045  without a resultant stress on the flow tube. In other words, the change in length of balance bar segments  1002  and  1003  results in only a flexing of the leaf springs  1045  and does not result in any stress being applied to flow tube  1001  other than that associated with the small force required to flex springs  1045 . 
     FIG. 12 discloses the details of brace bar  1010  and its lateral projections  1001 A which tightly couple the lateral sides of flow tube  1001  to the lateral sides of the inner wall  1002 A of balance bar segments  1002 ,  1003 . This coupling raises the frequency of undesired lateral vibrations of the flow tube so that they do not interfere with the drive frequency signals from the velocity sensors. 
     The embodiment of FIGS. 10,  11 , and  12  has a good thermal response since flexible springs  1045  permit the balance bar segments  1002  and  1003  to freely change in length without imparting a resultant stress to flow tube  1001 . The center drive coil bracket  1040  has a minimum of spurious vibration modes. Leaf springs  1045  couple the inner ends  1036  and  1037  of balance bar segments  1002  and  1003  so that they are prevented from having significant out of phase motion with respect to each other. As a result, Coriolis-like deflections are not induced in balance bar segments  1002  and  1003 . Thus the embodiment of FIGS. 10,  11 , and does not have the material flow sensitivity of the previously described embodiments. 
     Masses  1035  and  1041  provide for increased accuracy by making symmetrical the mass distribution about the plane perpendicular to the drive plane and containing the flow tube axis. Thus, mass  1041  weighs the same as drive coil  1044  plus driver drive coil bracket  1042 . Without these added masses a vibration imparted to the meter in the axial direction results in an erroneous flow signal because it imparts a Coriolis-like deflection to the balance bar. 
     The remainder of the Coriolis flowmeter shown on FIGS.  10 , 11 , and  12  is similar to that already described for the prior embodiments. These elements include case  1004 , case ends  1008  and  1009 , case necks  1005  and  1015 , flow tube inlet  1006  and flow tube outlet  1007 , cone connect elements  1013  and  1014 , inactive portions  1001 A and  1001 B of flow tube  1001 , case connect links  1031  and  1032  having side extremities  1033  connected to the inner wall  1020  of case  1004 , pick offs LPO and RPO, a pair of drivers D 1  and D 2 , drive coil brackets  1042  and  1043 , masses  1041  and  1035 , out of plane bends  1034  in case connect links  1031  and  1032 . 
     In the same manner as described for the embodiment of FIG. 1, meter electronics  121  applies a signal over path  123  to Driver D to vibrate balance bar  102  and flow tube  101  in phase opposition. Pick offs LPO and RPO detect the vibrations of the flow tube  101  with material flow and generate output signals indicating the magnitude and phase of the Coriolis response. The pick off and output signals are applied over paths  122  and  124  to meter electronics  121  which generates an output on path  125  containing information regarding the material flow. 
     In summary with respect to the embodiment of FIGS. 10,  11  and  12 , flexible drive coil bracket  1040  intermediate balance bar end segments  1002  and  1003  is advantageous in that springs  1045  easily flex and protect flow tube  1001  from axial stress in response to changes in the axial length of balance bar end segments  1002  and  1003 . Unlike the previous embodiments, the leaf springs of this embodiment do not lower the frequency of the Coriolis-like deflection enough to increase the sensitivity of the flow meter. 
     It is to be expressly understood that the claimed invention is not to be limited to the description of the preferred embodiment but encompasses other modifications and alterations within the scope and spirit of the inventive concept. For example, although the present invention has been disclosed as comprising a part of a single straight tube Coriolis flowmeter, it is to be understood that the present invention is not so limited and may be used with other types of Coriolis flowmeters including single tube flowmeters of irregular or curved configuration as well as Coriolis flowmeters having a plurality of flow tubes.