Patent Publication Number: US-2021190609-A1

Title: Measuring system and method for determining a force and/or a torque on a torque-transmitting shaft

Description:
The invention relates to a measuring system for determining a force and/or a torque on a torque-transmitting shaft, wherein the measuring system comprises at least three, in particular at least four, piezoelements, each having a preferred direction which are each arranged at different positions about a rotational axis of the shaft in a force flow transmitted via the shaft such that a force of the force flow acts, in particular exclusively, on the piezoelements. 
     In the development and regulation of motors, in particular internal combustion engines or electrical machines, it is important to have the most accurate knowledge possible about the torque on the shaft of the motor, in particular in test bench operation. 
     Employing measuring devices having strain gauges or piezoelectric sensors to that end is known from the prior art. 
     Strain gauges and similar measuring elements generally serve in measuring static forces. Generally speaking, however, measuring systems with measuring elements of this type have a reaction time which is too long for measuring dynamic force paths. In contrast, piezoelectric measuring elements, or piezoelements respectively, are suited to measuring dynamic tensile, compressive and shear forces. They have a broad dynamic range, are rigid, and can also measure highly dynamic forces with concurrently high resolution. 
     Document EP 0 266 452 A1 relates to a piezoelectric transducer for measuring force and torque which consists of at least two piezoelements as well as at least one carrier plate made of insulating material arranged between them, wherein the piezoelements are crystallographically preorientated with respect to the coordinate system of the carrier plate and fixedly connected to same. 
     The DE 195 25 22 A1 document relates to a force and torque measuring arrangement consisting of a plurality of force-measuring cells and amplifier arrangements, characterized in that the plurality of force-measuring cells are tightly screwed to a measuring unit between mounting plates and arranged with respect to coordinate axes such that torque formation is possible, whereby the signals from the force-measuring cells are routed to a group of amplifiers for evaluation and their outputs are in turn routed to a group of operational amplifiers, as a result of which both the individual force components as well as the moments of force can be measured. 
     Document DE 10 2009 014284 B4 relates to a torque sensor consisting of a first and a second disc-shaped fastening flange which are disposed axially opposite one another in parallel and connected together rigidly by a radially inward torque transmission element, wherein the second fastening flange is designed as a measuring flange exhibiting a plurality of recesses and shear force transducers separated from each other by radial stiffening webs on a coaxial circumferential region between its radially outer fastening area and the coaxially inward torque transmission element, wherein the recesses are formed by at least three measuring pockets which are axially open on one side, wherein the base area of the measuring pockets is formed as a flat closed surface representing a uniformly thin, spring-elastic deformation body and the shear force transducers are applied on the base surfaces or the axially opposed outer surfaces of the measuring pockets. 
     It is a task of the invention to provide improved determination of an applied torque or an applied force on a torque-transmitting shaft. In particular, it is a task of the invention to provide an easily calibrated measuring system. 
     This task is solved by a measuring system for determining a force and/or a torque, a method for determining a torque applied to a torque-transmitting shaft and/or a force acting on a shaft, and a method for calibrating a measuring system in accordance with the independent claims. Advantageous embodiments are claimed in the subclaims. 
     A first aspect of the invention relates to a measuring system for determining a force and/or torque on a torque-transmitting shaft, wherein the measuring system comprises at least three, in particular at least four, piezoelements, each having a preferred direction, which are each arranged at different positions about a rotational axis of the shaft in a force flow transmitted via the shaft such that a force of the force flow acts, in particular exclusively, on the piezoelements, wherein the preferred directions each lie parallel to or in a single plane intersected by the rotational axis, and wherein the preferred directions of at least two, in particular at least three, of the piezoelements are oriented neither parallel nor antiparallel to one another. Given two parallel or antiparallel preferred directions, the two preferred directions are preferably oriented perpendicular to each other. 
     The features and advantages described below with respect to the first aspect of the invention also apply to the further aspects of the invention and vice versa. 
     A force flow in the sense of the invention is a path of a force and/or torque in a mechanical system from a point of application, in particular a point of introduction, to one point or multiple points at which force and/or torque is taken up by a reactive force and/or reactive torque. Preferably, the force flow is composed of a force, in particular a force transverse to the shaft&#39;s rotational direction, and a torque, in particular about the rotational axis. 
     A power flow in the sense of the invention is a path of power transmission in a mechanical system from a point of introduction to one point or multiple points at which the power drops off. 
     A fixing device in the sense of the invention serves preferably in bearing, in particular fixing, the piezoelements. Further preferably, the fixing device connects the individual piezoelements, whereby they are held in a relative position to one another. Preferably, the fixing device is an adapter plate, a ring element, a measuring flange or even a mounting bracket. Further preferably, the fixing device can be a component of an existing apparatus, for example a housing, a gearbox or a machine. 
     A piezoelement in the sense of the invention is preferably a measuring element configured to measure a force acting over two areas adjacent the piezoelement. Preferably, a piezoelement consists of the piezoelectric crystal as well as a charge dissipator or electrical circuit respectively. 
     A measuring system in the sense of the invention is preferably a piezoelectric sensor. In this case, the measuring system serves as the housing of the piezoelements. 
     Alternatively, however, the measuring system can also comprise individual piezoelectric sensors, whereby the piezoelements are arranged in a separate housing. 
     A machine in the sense of the invention is configured to convert energy, preferably kinetic energy, in particular a rotation, into electrical energy or vice versa, or chemical energy into kinetic energy. A machine within the meaning of the invention preferably exhibits a housing. 
     A bearing apparatus in the sense of the invention is preferably an apparatus for rotatably supporting a shaft, in particular a roller bearing, ball bearing or slide bearing. Preferably, a bearing apparatus also exhibits a housing. The bearing apparatus itself is preferably also in turn itself supported or mounted. Further preferably, the bearing apparatus according to the invention is a machine or part of a machine. 
     A supporting apparatus in the sense of the invention is preferably an apparatus for supporting an element against a force and/or a torque acting on said element. A supporting apparatus is to that end preferably configured to provide a so-called reactive force or bearing reaction force respectively. A supporting apparatus within the meaning of the invention serves preferably in supporting the bearing apparatus. Preferably, the supporting apparatus is a bell housing, a drivetrain housing or a base plate. 
     The term “mountable” within the meaning of the invention means “able to be mounted” or “being mounted.” 
     The term “connectable” within the meaning of the invention means “able to be connected” or “being connected.” 
     The term “introducible” within the meaning of the invention means “able to be introduced” or “being introduced.” Preferably, this thereby refers to the transmitting of a force from one body to another body. 
     The term “supportable” within the meaning of the invention means “able to be supported” or “being supported.” 
     The term “guidable through” within the meaning of the invention means “able to be guided through” or “being guided through.” 
     The term “loadable” within the meaning of the invention means “able to be loaded” or “being loaded.” 
     The term “arrangeable” within the meaning of the invention means “able to be arranged” or “being arranged.” 
     The invention is based in particular on the approach of determining forces and/or torques acting on a torque-transmitting shaft via a system of equations for force components and torque components based on measurement signals of the individual measuring elements. 
     To that end, the preferred directions of at least three piezoelements must each lie parallel to or in a plane intersected by a rotational axis of the shaft. Preferably, this plane is oriented approximately perpendicular to the shaft&#39;s rotational axis. Furthermore, the preferred directions of the three piezoelements must be oriented such that different force components are measured at different points. Therefore, at least two, preferably three, preferred directions are not to be oriented parallel or antiparallel to one another. 
     The cited arrangement allows the measurement signals of at least two piezoelements to be separated into linearly independent components. In particular, any force and any torque in the plane acting on the shaft can be determined by way of the measurement signals from piezoelements arranged as such. 
     With the measuring system according to the invention, all the piezoelements can be employed in determining the force or the torque by taking into account the contribution of individual piezoelements to different force components and torque components. 
     This avoids the need for respectively different piezoelements or piezoelement groups when determining different directions of force and/or torque. This is advantageous since piezoelements which do not contribute to the measurement of a force component or the torque represent a force shunt with respect to these force components or torque which distorts the measurement result. In the inventive measuring system, a force shunt results at most from fixing means used to fix the piezoelements. 
     Those portions of a piezoelement&#39;s measurement signals which do not contribute to the respectively considered force component or torque are not taken into account according to the invention. A paired arrangement of piezoelements having antiparallel preferred directions to cancel out unwanted portions of the measurement signals is therefore not necessary with the inventive measurement system. 
     Preferably, the measuring system is thereby configured to measure forces acting both tangential to the shaft&#39;s rotational direction, which contribute to the torque, as well as transverse forces, which act perpendicular to the shaft&#39;s rotational direction, particularly in two orthogonal directions in the plane, and which can contribute to wobbling of the shaft. 
     Preferably, any number of piezoelements can also be inventively used to determine the individual directions of the force or the torque. Measurement accuracy can thereby be significantly increased. 
     Using piezoelements in the measuring enables the registering of highly dynamic changes in force or torque respectively. 
     Should more than three piezoelements be used for the measurement, measurement accuracy can be increased even more. The same applies when more than two preferred directions of the piezoelements are oriented neither parallel nor antiparallel to each other. 
     In one advantageous embodiment of the measuring system according to the invention, in particular having more than three piezoelements, the piezoelements are geometrically arranged such that there is no mirror axis and/or point of symmetry in terms of their respective position relative one another in a projection onto the plane. 
     The inventive measuring system in particular enables arrangements of piezoelements not needing to be arranged in mirror-inverted pairs. The asymmetry of the piezoelement arrangement enables a particularly exact determination of the force or the torque. 
     Preferably, the preferred direction of at least one piezoelement is not tangential to a direction of rotation of the shaft. 
     In a further advantageous embodiment of the measuring system, the piezoelements are geometrically arranged such that at least two piezoelements have a different radial distance from the rotational axis and/or that two circular sectors around the rotational axis between two respective piezoelements span a different angle. 
     This, too, ensures a high degree of asymmetry to the arrangement of the piezoelements and thus increases the measurement accuracy. 
     In a further advantageous embodiment, the inventive measuring system further comprises a signal processing device which is configured to determine the force and/or torque on the shaft by means of decomposition, in particular orthogonal decomposition, of the respective preferred direction of the piezoelements or the forces to be measured by the individual piezoelements in at least two components, whereby respective parallel components are added together. Preferably, a first component is thereby at least substantially tangential to the shaft&#39;s direction of rotation and a second component is preferably at least substantially perpendicular to the direction of rotation. 
     Decomposition of the preferred direction or the forces enables a plurality of piezoelement measurement signals to be taken into account, each of which contributes to the measurement signal or respectively to the force in a defined direction. 
     Even if the system of equations solution for three piezoelements arranged pursuant to the invention is unique, the more piezoelements taken into account in the equation system, the more exact of a system resolution can be achieved. Preferably, the force components and/or the torque are to that end calculated from combinations of three respective measurement signals and then averaged across the number of combinations. 
     The decomposition of the measurement signal into components of the preferred direction or the force moreover has the advantage of not needing to know the exact installation scenario of the piezoelements with respect to the preferred direction of the individual piezoelements. Nor does the arrangement of the piezoelements with respect to the shaft, in particular their radial distance, need to be known. Both parameters can in this case be determined by calibration measurements. 
     Preferably, measurement signals from all the piezoelements having a respective preferred direction lying parallel to or in the plane are used to determine the force and/or the torque. This thereby prevents portions of the force flow from being lost through a force shunt of a sensor not involved in the measurement. 
     In a further advantageous embodiment of the inventive measuring system, the plane is oriented at least substantially perpendicular to a rotational axis of the shaft. 
     Due to this orientation of the plane and the associated orientation of the preferred directions of the piezoelements, a particularly high resolution of the measurement in terms of the torque and forces transverse to the rotational direction can be realized. If the plane is not perpendicular to the rotational axis, measurement signals are only taken into account on a proportional basis to determine the transverse forces and the torque. The portions thereby correspond in each case to the projection of the preferred direction of the respective piezoelement on a fictitious plane which is normal or respectively perpendicular to the rotational axis. 
     In a further advantageous embodiment of the inventive measuring system, an area of the piezoelements over which the force is introduced lies at least substantially parallel to the plane. As a result, there can be a particularly good introduction of shear forces into the piezoelement. 
     In a further advantageous embodiment of the inventive measuring system, the piezoelements form a main direct force relative to the force flow, and a force shunt, in particular on fixing means, takes in less than 10%, preferentially less than 5%, and most preferentially less than 2% of the force of the force flow. This thereby enables a particularly precise determination of the force and/or the torque. 
     In a further advantageous embodiment of the inventive measuring system, a further piezoelement with a preferred direction not oriented parallel to the plane, in particular at least substantially perpendicular to the plane, is arranged adjacent each piezoelement in the direction of the shaft&#39;s rotational axis, whereby the piezoelements form pairs with the respective adjacently arranged further piezoelement, wherein the force of the force flow acts in particular substantially on the pairs. 
     By providing these further piezoelements, not only can a two-dimensional measurement be made of components in the plane but all of the force components can be measured in three dimensions. This is particularly useful when compressive or tensile forces are also to be determined in the direction of the shaft&#39;s rotational axis. Due to the particularly advantageous paired arrangement with those piezoelements having a preferred direction arranged parallel to or in the plane, a force shunt is kept as minimal as possible or even completely prevented here as well. 
     In a further advantageous embodiment, the measuring system comprises a fixing device, in particular a bearing cage, whereby the fixing device supports the piezoelements and positions them relative to each other. 
     By providing such a fixing device, the measuring system can be utilized as a closed unit in which the individual piezoelements have a fixed position relative to one another. In particular, such a measuring system can be precalibrated, whereby the orientation of the individual preferred directions of the piezoelements and the position of the individual piezoelements are predefined in a reference system of the fixing device. Further preferably, the piezoelements are at least 50%, preferentially at least 70%, even more preferentially at least 90% accommodated in a depression, in particular a blind hole, on the fixing device. 
     In a further advantageous embodiment of the inventive measuring system, the piezoelements are unevenly distributed about the rotational axis. This thereby enables realizing measurement arrangements in which torque cannot be determined at all circumferential points around the rotational axis for structural reasons. 
     In a further advantageous embodiment, all the piezoelements and/or pairs within a defined circular sector about the rotational axis are arranged at an angle α&lt;300°, preferentially α&lt;240°, further preferentially α&lt;180°, most preferentially α&lt;120°, wherein a fixing device is preferably designed so as to cover this angular sector. 
     In a further advantageous embodiment of the inventive measuring system, the shaft is supported by a bearing apparatus, in particular a machine, the output and/or input shaft of which is formed by the torque-transmitting shaft, whereby a fixing device supports the piezoelements and/or pairs and is designed such that a force, in particular a shear force, is measurable between the bearing apparatus and a supporting apparatus for supporting the bearing apparatus via the piezoelements. 
     This embodiment does away with the need for forces and/or torques acting on the torque-transmitting shaft to be measured directly on said shaft. 
     In particular, there is no need to arrange for a measuring apparatus which is screwed or otherwise attached to the torque-transmitting shaft, as is for example described in the initially cited DE 2009 014 284 B4. On the contrary, this embodiment measures those forces acting as reactive forces on a bearing apparatus of the shaft and the force exerted by the shaft, or the torque acting on the shaft respectively, is deduced from said forces. In other words, the forces are inventively measured at a point in the force flow other than on the torque-transmitting shaft, yet outside of the power flow, and the torque acting on the torque-transmitting shaft is determined, in particular calculated, from said forces. 
     Due to the strength and rigidity of the piezoelements employed as measuring elements, the bearing apparatus can for one thing be preferably completely supported or mounted by means of the piezoelements. Preferably the full load or full force flow respectively is thus on the piezoelements in this embodiment as well - secondary force flows can at the least be ignored. 
     In this embodiment, the measuring system does not distort the measurement result since the measuring system is not a component of the rotating shaft. In particular, there is no altering of the moving mass or rotating mass respectively of a torque-transmitting system to be measured, in particular a system to be tested on the test bench. Nor does the measuring apparatus add any elasticities to the torque-transmitting system which would act as vibration dampers or would influence, in particular distort, the natural frequencies of the torque-transmitting system. This is in particular an advantage of the piezoelements compared to systems with strain gauges as measuring elements which, due to their design, are relatively flexible compared to piezoelements and thus influence the system under testing. 
     The embodiment further enables analyzing the movement of the torque-transmitting shaft and identifying discontinuities and vibrations in the shaft&#39;s motion. In particular, a wobbling of the shaft can be identified and measured. This is not possible, or is only possible with difficulty, with a measuring system such as a measuring flange arranged on the shaft. In particular, there is no guarantee that such a measuring flange will be located at that point on the shaft which actually wobbles. The invention is also able to determine the forces which the torque-transmitting shaft exerts on its bearing apparatus and/or a machine, in particular a motor. Such forces cannot be measured with a measuring flange and cannot be determined, or at least not precisely, from the available measurements. 
     The configuration can thus determine dynamic torque applied to the shaft as well as vertical and horizontal vibrations in the shaft. 
     In a further advantageous embodiment, the fixing device is further designed such that the force can be introduced parallel to end faces of the piezoelements and/or pairs via a non-positive connection. 
     This embodiment provides the possibility of using a piezoelectric shear element as the piezoelement. In particular, a single piezoelement can thereby measure forces in two opposite directions without the need for a bonded connection to be established between the end faces of the piezoelements and the respective force-introducing elements. 
     Preferably, the piezoelements can be frictionally connected to the fixing device and/or bearing apparatus and/or supporting apparatus. Further preferably, the fixing device is further designed such that a force can be measured at least substantially tangential to the direction of rotation and/or parallel to the rotational axis of the shaft. 
     In a further advantageous embodiment of the inventive measuring system, the piezoelements each exhibit a cavity, in particular a hollow cylinder, through which a respective fixing device, in particular a tensioning screw, can be guided. 
     In a further advantageous embodiment of the inventive measuring system, the fixing device also exhibits cavities which are at least partially aligned with the cavity of the piezoelectric sensor and in which the tensioning screw can be seated. 
     By cavities being provided in the piezoelements and/or the fixing device, in particular a pretensioning or respectively preloading can be applied to the piezoelements by means of the fixing devices, whereby a non-positive connection can be established between their end faces and a further element. 
     A second aspect of the invention relates to a test bench or a vehicle having a measuring system according to the first aspect of the invention. 
     A third aspect of the invention relates to a measuring arrangement for determining a force and/or a torque on a torque-transmitting shaft which comprises a measuring system based on the piezoelectric effect and a shaft, wherein the piezoelements are arranged between a first part of the shaft and a second part of the shaft such that a force, in particular a shear force, can be measured between the first part and the second part by means of the piezoelements. 
     In one advantageous embodiment of the measuring arrangement, the shaft consists of two sections able to be connected via a coupling device, whereby the measuring system determines the force and/or torque on one of the two sections. 
     A fourth aspect of the invention relates to a measuring arrangement for determining a force and/or a torque on a torque-transmitting shaft which comprises a measuring system based on the piezoelectric effect, a shaft, a bearing apparatus and a supporting apparatus of the bearing apparatus, wherein the bearing apparatus supports the shaft, and wherein the measuring system does not alter a rotating mass of the shaft and/or a rotating mass of rotating parts of an aggregate consisting of the shaft and the bearing apparatus. Preferably, a measuring system is thereby used via which the reactive forces of a bearing of the shaft can be measured. 
     Preferably, the bearing apparatus is thereby a machine, in particular a dynamometer and/or prime mover, preferably an electrical machine or internal combustion engine. 
     A fifth aspect of the invention relates to a method for determining a torque applied to a shaft and/or a force applied to a shaft, wherein the force and/or torque on the shaft is determined by means of orthogonal decomposition of the respective preferred directions of the piezoelements or the respective forces measured by the individual piezoelements, whereby respective parallel components are added together. 
     In one advantageous embodiment, the method comprises the following procedural steps: detecting at least one first signal of a first piezoelectric sensor, one second signal of a second piezoelectric sensor, and one third signal of a third piezoelectric sensor; 
     proportionately totaling the signals in at least one direction corresponding to a respective component of the preferred direction of the piezoelements in said direction; and deriving the torque and/or force from the summed signals; or 
     proportionately deriving the torque and/or force for each individual signal in at least one direction corresponding to a respective component of the preferred direction of the piezoelements in said direction; and 
     totaling the torques and/or forces. 
     A sixth aspect of the invention relates to a method for calibrating a measuring system comprising the following procedural steps: 
     applying a defined force in a first direction parallel to the plane; 
     applying a defined force in a second direction parallel to the plane; 
     detecting at least one first signal of a first piezoelectric sensor, one second signal of a second piezoelectric sensor, and one third signal of a third piezoelectric sensor; and 
     deriving preferred directions of the piezoelements on the basis of the detected signals and first and second direction of the defined forces. 
     A seventh aspect of the invention relates to a method for calibrating a measuring system comprising the following procedural steps: 
     applying a defined torque about the rotational axis of the shaft; detecting at least one first signal of a first piezoelectric sensor, one second signal of a second piezoelectric sensor, and one third signal of a third piezoelectric sensor; and 
     deriving distances of the piezoelements, in particular in relation to the rotational axis of the shaft of the piezoelements, on the basis of the detected signals and the defined torque. 
     Further aspects of the invention relate to a computer program which is configured to, when run on a computer, prompt the latter to execute the steps of a method according to the invention, as well as a corresponding computer-readable medium. The inventive methods can thus be computer-supported. 
     Further advantages and features will become apparent from the preferential exemplary embodiments described below with reference to the figures. The figures show, at least partially schematically: 
       FIG. 1  a first exemplary embodiment of a measuring arrangement for determining a force and/or a torque on a torque-transmitting shaft; 
       FIG. 2  an arrangement of piezoelements of a first exemplary embodiment of a measuring system; 
       FIG. 3  an arrangement of piezoelements of a second exemplary embodiment of a measuring system; 
       FIG. 4  an arrangement of piezoelements of a third exemplary embodiment of a measuring system; 
       FIG. 5  a perspective view of a fourth exemplary embodiment of a measuring system; 
       FIG. 6  a second exemplary embodiment of a measuring arrangement; 
       FIG. 8  a fourth exemplary embodiment of a measuring arrangement; 
       FIG. 9  a perspective view of a detail of a measuring arrangement with a measuring apparatus as per the fourth exemplary embodiment according to  FIG. 8 ; 
       FIG. 10 a    a plan view and a cross-sectional view of a fifth exemplary and  10   b  embodiment of a measuring system; 
       FIG. 11 a    a perspective view and a cross-sectional view of a sixth exemplary and  11   b  embodiment of a measuring system; and 
       FIG. 12  a circuit diagram of a measuring system corresponding to all the exemplary embodiments. 
    
    
       FIG. 1  shows a plan view of a first exemplary embodiment of a measuring arrangement  9  for determining a force and/or a torque on a torque-transmitting shaft  3   a ,  3   b  on a drive test bench  15 . The shaft  3   a ,  3   b  thereby connects a motor  2 , which among other things serves as a bearing apparatus for the shaft  3   a ,  3   b , to a gearbox and differential  13 , which is in turn connected to wheel dynamometers  14   a ,  14   b  via axle sections. 
     A measuring system  1  having a measuring flange  5   a ,  5   b  consisting of two parts is arranged as a fixing device between a first section  3   a  of the shaft and a second section  3   b  of the shaft. The first section  3   a  of the shaft is non-rotatably connected to a first part  5   a  of the measuring flange and the second section  3   b  of the shaft is non-rotatably connected to a second part  5   b  of the measuring flange. Three piezoelements  4   a ,  4   b ,  4   c  are arranged between the two parts  5   a ,  5   b  of the measuring flange and likewise fixedly attached to the parts  5   a ,  5   b  of the measuring flange, in particular by means of a non-positive connection. 
     With this measuring arrangement  9 , a force can flow from a supporting apparatus  10  (not depicted) via the motor  2 , the first section of the shaft  3   a , the first part  5   a  of the measuring flange, the three piezoelements  4   a ,  4   b ,  4   c , the second part  5   b  of the measuring flange and the second section  3   b  of the shaft, the gearbox and differential  13  and the axle components to the wheel dynamometers  14   a ,  14   b , themselves in turn supported by suitable means. A potential power flow thereby runs from the motor  2  to the wheel dynamometers  14   a ,  14   b  via the shaft  3   a ,  3   b  and the measuring flange  5   a ,  5   b  as well as the gearbox and differential  13 . 
     An applied force is introduced into the piezoelements or respectively applied to the piezoelements  4   a ,  4   b ,  4   c , in particular by way of end faces of the piezoelements  4   a ,  4   b ,  4   c , via the components of the measuring flange  5   a ,  5   b . The measuring system  1  is shown in  FIG. 1  in a plan view of a plane spanned by the y-axis and the z-axis of a depicted reference system. 
       FIG. 2  shows an arrangement of piezoelements  4   a ,  4   b ,  4   c  of a first exemplary embodiment of a measuring system  1  as can be used for example in the first exemplary embodiment of a measuring arrangement  9  according to  FIG. 1 . 
     The arrangement of the piezoelements  4   a ,  4   b ,  4   c  is thereby shown in a plane spanned by the y-axis and the x-axis of the reference system according to  FIG. 1 . The end faces  17   a ,  17   b ,  17   c  of the piezoelements are therefore visible. 
     The center points of the piezoelements  4   a ,  4   b ,  4   c  are all arranged at a distance d from the center point through which the rotational axis D of a shaft  3  (not depicted) runs. Each of the piezoelements  4   a ,  4   b ,  4   c  thereby occupies a different position about the rotational axis D or the center point respectively. The dash/dotted circle encircles the shaft, or center point respectively, and indicates the rotational direction of the piezoelements  4   a ,  4   b ,  4   c  at each point about the rotational axis D, or center point respectively, upon rotation of the shaft  3  (not depicted). 
     Each of the piezoelements  4   a ,  4   b ,  4   c , exhibit a different preferred direction V a , V b , V c  in a plane spanned by the x-axis and the y-axis. Preferably, the three preferred directions V a , V b , V c  point in different directions and are thus oriented neither parallel nor antiparallel. Further preferably, however, only two of the three preferred directions V a , V b  are oriented neither parallel nor antiparallel. The third preferred direction V c  can in this case be oriented parallel to one of the two other preferred directions V a , V b . 
     Angular sectors  19   a ,  19   b ,  19   c  in relation to rotational axis D span between the positions of the individual piezoelements  4   a ,  4   b ,  4   c . Angular sector  19   a  between a first piezoelement  4   a  and a second piezoelement  4   b  thereby exhibits angle α ab , angular sector  19   b  between the second piezoelement  4   b  and a third piezoelement  4   c  exhibits angle α bc , and angular sector  19   c  between the third piezoelement  4   c  and the first piezoelement  4   a  exhibits angle α ca . 
     Preferably, at least two of the angles α ab , α bc , α ca  of the angular sectors have different values. 
     All of the piezoelements  4   a ,  4   b ,  4   c  have a bore  21   a ,  21   b ,  21   c  through which a fixing means, in particular a bolt or a screw (not depicted), can be guided. A shear force can be introduced via the end faces  17   a ,  17   b ,  17   c.    
       FIG. 3  shows an arrangement of piezoelements  4   a ,  4   b ,  4   c  of a second exemplary embodiment of a measuring system  1 . 
     As in  FIG. 2 , the piezoelements are depicted in a plan view onto the end faces  17   a ,  17   b ,  17   c ,  17   d . The viewing direction in  FIG. 3  is likewise perpendicular to the plane spanned by the x-axis and the y-axis of the reference system (α ab , α bc , α ca ) and the arrangement according to  FIG. 2  can also be used in a measuring arrangement  9  of  FIG. 1 . 
     The preferred directions V a , V b , V c , V d  of the individual piezoelements  4   a ,  4   b ,  4   c ,  4   d  point in different directions in the arrangement of piezoelements  4   a ,  4   b ,  4   c ,  4   d  and are not tangential to the direction of rotation, indicated by the dashed circle, yet also lie, as in  FIG. 2 , in a plane spanned by the x-axis and the y-axis of the reference system and thus perpendicular to a shaft  3  (not depicted), the rotational axis D of which runs through the center point out of the image plane. 
     The preferred direction V b  of the second piezoelement  4   b  is oriented antiparallel to the preferred direction V d  of the fourth piezoelement  4   d  in the depicted arrangement. 
     As in  FIG. 2 , all of the piezoelements  4   a ,  4   b ,  4   c ,  4   d  have a bore  21   a ,  21   b ,  21   c ,  21   d  through which a fixing means, in particular a bolt or a screw (not depicted), can be guided. A shear force can be introduced via the end faces  17   a ,  17   b ,  17   c ,  17   d.    
       FIG. 4  shows a third arrangement of four piezoelements  4   a ,  4   b ,  4   c ,  4   d  for a third exemplary embodiment of a measuring system, as can likewise be used in a measuring arrangement  9  according to  FIG. 1 . 
     In contrast to the arrangements of  FIGS. 2 and 3 , the piezoelements  4   a ,  4   b ,  4   c ,  4   d  are at different distances R a , R b , R c , R d  from the center point D of the arrangement through which the shaft  3  (not depicted) would run in a measuring system. Rotational direction of the piezoelements  4   a ,  4   b ,  4   c ,  4   d  about rotational axis D, or the center point respectively, is again indicated by dashed/dotted circles. 
     The preferred directions V a , V b , V c , V d  of the piezoelements  4   a ,  4   b ,  4   c ,  4   d  respectively run tangential to the direction of rotation. 
     In contrast to  FIG. 3 , the piezoelements  4   a ,  4   b ,  4   c ,  4   d  are furthermore unevenly arranged over the circumference around the rotational axis D, or the center point respectively. 
       FIG. 5  shows a further arrangement of sensors of a fourth exemplary embodiment of the measuring system  1 . 
     In the depicted measuring system  1 , the individual piezoelements  4   a ,  4   b ,  4   c ,  4   d  are supported by a fixing device  5 . The preferred directions V a , V b , V c , V d  of the piezoelements  4   a ,  4   b ,  4   c ,  4   d  are preferably oriented to the course of the fixing device  5 , although can also point in other directions as long as each of the preferred directions V a , V b , V c , V d  lies parallel to or in a single plane, in particular that plane which is also defined by the fixing device  5 . 
     The rotational axis D of a shaft  3  (not depicted) to which a force and/or torque is applied (not depicted) is arranged in this exemplary embodiment in an area to the left of the fixing device  5  in relation to  FIG. 5 . The dashed/dotted line indicates one such possible rotational axis D. 
     The rotational axis D does not thereby have to be arranged at the same distance from each of the piezoelements  4   a ,  4   b ,  4   c ,  4   d , nor does the rotational axis D have to run through a center point defined as applicable by the curvature of the fixing device  5 . 
       FIG. 6  shows a second exemplary embodiment of a measuring arrangement  9  on a test bench  15 . 
     Differing from the measuring arrangement  9  according to  FIG. 1 , the measuring arrangement  9  of  FIG. 6  further comprises a coupling  6   a ,  6   b.  A first coupling part  6   a  is thereby non-rotatably connected to the second part  5   b  of the measuring flange and can be releasably brought into non-positive contact with a second coupling part  6   b.    
     Depending on the position of the coupling plates  6   a ,  6   b  relative to one another and the outputs to be transmitted in the force flow from the motor  2  to the wheel dynamometers  14   a ,  14   b , a torque to be determined is applied to the measuring flange  5   a ,  5   b.    
       FIG. 7  shows a third exemplary embodiment of a measuring arrangement  9  on a test bench  15 . 
     Unlike with the measuring arrangement  9  according to  FIGS. 1 and 6 , force and/or torque is not measured in the power flow between the motor  2  and the wheel dynamometers  14   a ,  14   b , or between the motor  2  and the gearbox and differential  13  respectively. Instead, the torque and/or forces acting on the torque-transmitting shaft  3  are determined outside of the power flow via the reactive forces with which the motor  2  is supported on the test bench by a supporting apparatus  10 . 
     The piezoelements are accordingly arranged in the flow of force between the supporting apparatus  10  and the motor  2 . 
     As in the other exemplary embodiments having a measuring flange  5   a ,  5   b  in the shaft  3 , a torque-transmitting connection is also established here between the piezoelements  4   a ,  4   b ,  4   c  and the motor  2  as well as the supporting apparatus  10  by the piezoelements  4   a ,  4   b ,  4   c , or their end faces respectively, forming a non-positive connection with corresponding sections of the motor  2  and the supporting apparatus  10 . 
       FIG. 8  shows a fourth exemplary embodiment of a measuring arrangement  9  which can in particular be used in a vehicle. 
     In contrast to the exemplary embodiment according to  FIG. 7 , the supporting apparatus  10  in this exemplary embodiment is designed as a type of bell housing. The motor  2  is therefore supported on a housing  8  of the gearbox and differential  13 . 
     The flow of force in this exemplary embodiment thus runs from the gearbox housing  13  via the bell housing  10  to the motor  2  and from there via the torque-transmitting shaft and the gearbox and differential  13  to the wheel dynamometers  14   a ,  14   b.    
     The piezoelements  4   a ,  4   b ,  4   c  here are also arranged outside of the power flow between the motor  2  and the bell housing  10  in order to transmit a reactive force and/or torque. Here as well, a non-positive connection is formed between the corresponding surfaces of the motor  2  and bell housing  10  and the piezoelements  4   a ,  4   b ,  4   c.    
     Preferably, each of the arrangements of piezoelements  4   a ,  4   b ,  4   c ,  4   d  of the different exemplary embodiments of a measuring system  1  shown in  FIGS. 2 to 5  can be used in the exemplary embodiments for measuring arrangements  9  shown in  FIGS. 6 to 8 . 
     As an example,  FIG. 9  shows the use of a measuring system according to  FIG. 5  in the fourth exemplary embodiment of a measuring arrangement  9  according to  FIG. 8 . The measuring system  1  with the fixing device  5  and piezoelements  4   a ,  4   b ,  4   c ,  4   d  is arranged on a bell housing  10  in this plan view. 
     Preferably, the measuring system  1  is thereby supported on the bell housing  10  by fixing means  16   a ,  16   b ,  16   c ,  16   d.  Moreover, the fixing means  16   a ,  16   b ,  16   c ,  16   d  serve to produce a pretensioning between the motor  2  (not shown) and the bell housing  10  so that the respective end faces of the piezoelements  4   a ,  4   b ,  4   c ,  4   d  come into contact with a surface of the bell housing  10  and a surface of the motor  2  to form a non-positive connection. 
     Due to the friction between the piezoelements  4   a ,  4   b ,  4   c ,  4   d  and the motor  2  and supporting apparatus  10 , shear forces can be introduced to the piezoelements via the end faces of said piezoelements which effect a separation of charge in the piezoelements  4   a ,  4   b ,  4   c ,  4   d . As a result, there are shear force-dependent potentials on the charge dissipators or electrical lines  22  respectively. 
     A shaft  3  (not depicted) can extend through the bell housing  10  in the direction of the gearbox and the differential  13  through an opening  11  in said bell housing  10 . 
       FIGS. 10 a  and 10 b    show a fifth exemplary embodiment of a measuring system  1  having piezoelement pairs  18   a ,  18   b ,  18   c ,  18   d  supported by a fixing device  5 . 
       FIG. 10 a    thereby shows a plan view onto the measuring system  1  and  FIG. 10 b    shows a cross-sectional view along line Y-Y. The piezoelement pairs  18   a ,  18   b ,  18   c ,  18   d  are in each case formed by two piezoelements  4   b ,  4   e ;  4   d ,  4   f  arranged adjacent one another in the direction of the rotational axis D of a torque-transmitting shaft  3  (not shown), the applied force and/or applied torque of which are to be determined. 
     A first piezoelement  4   b ,  4   d  of each piezoelement pair  18   a ,  18   b ,  18   c ,  18   d  thereby exhibits a preferred direction which is parallel to or in a single plane intersected by the rotational axis D of the shaft  3 , wherein the plane is preferably oriented perpendicular to the rotational axis D, as depicted in  FIG. 10 b   . Preferably forces and/or torque acting in this plane can be determined by means of these first sensors  4   b ,  4   d.    
     The further piezoelements  4   e ,  4   f  of the piezoelement pairs  18   a ,  18   b ,  18   c ,  18   d  preferably exhibit preferred directions which are not parallel to the plane and are further preferably perpendicular to said plane. Preferably compressive or tensile forces which are oriented substantially perpendicular to the direction of rotation D can therefore be measured with the further piezoelements  4   e ,  4   f.    
     As depicted in  FIG. 10 b   , each piezoelement pair has two end faces  17   b ,  20   b ;  17   d ,  20   d  respectively formed by one of the piezoelements  4   b ,  4   e ;  4   d ,  4   f.    
     The one end face  20   b ,  20   d  in each case is as a result seated in the fixing device  5 . The other end face  17   b ,  17   d  can come into contact with a component in respect of which a force is to be measured. Both end faces  17   b ,  17   d  as well as second end faces  20   b ,  20   d  thereby form a preferably non-positive, in particular frictional, connection with the fixing device and the other component. 
     As previously described, fixing means, in particular tensioning screws, can to that end be guided into the bores in the piezoelements through bores  21   a ,  21   b ,  21   c ,  21   d  in the piezoelement pairs  18   a ,  18   b ,  18   c ,  18   d , by means of which the fixing device and the respective other component and thereby also the piezoelement pairs  18   a ,  18   b ,  18   c ,  18   d  can be braced. Preferably, fixing device  5  as well exhibits cavities  12  in order to accommodate the fixing means. 
     Each of the piezoelements  4   a ,  4   b ,  4   c ,  4   d ,  4   e ,  4   f  generates a measurement signal S 1 , S 2 , S 3 , S 4 , S 5 , S 6  able to be picked up via charge dissapators  22 . 
       FIGS. 11 a  and 11 b    show a sixth exemplary embodiment of an inventive measuring system  1 .  FIG. 11 a    is thereby a perspective plan view and  FIG. 11 b    a cross-sectional view. 
     The measuring system  1  in this exemplary embodiment is characterized in that the piezoelements  4   a ,  4   b ,  4   c ,  4   d  are arranged between a first part of the flange  5   a  and a second part of the measuring flange  5   b , wherein a pretensioning is applied in the radial direction to the rotational axis D. This is in contrast to the exemplary embodiments of 
       FIGS. 1 to 5 and 10   a / 10   b  where the pretensioning and consequently the frictional connection is generated in the direction of rotational axis D. 
     Each of the piezoelements  4   a ,  4   b ,  4   c ,  4   d  generates a measurement signal S 1 , S 2 , S 3 , S 4  able to be picked up via charge dissipators. 
     Alternatively to a measuring flange  5   a ,  5   b , the depicted components respectively connected to the piezoelements  4   a ,  4   b ,  4   c ,  4   d  can also be a bearing apparatus  2  and a supporting apparatus  10  of a shaft  3  (not depicted). 
     As shown in  FIG. 12 , a measuring system  1  preferably comprises a signal processing device  7  for processing measurement signals S 1  of the first piezoelement  4   a , measurement signals S 2  of the second piezoelement  4   b , measurement signals S 3  of the third piezoelement  4   c  and measurement signals S 4  of the fourth piezoelement  4   d.    
     In order to be able to calculate the torque Mz on the shaft as well as transverse forces Fx, Fy, the signal processing device  7  preferably renders an orthogonal decomposition of the respective preferred direction V a , V b , V c , V d  of the piezoelements  4   a ,  4   b ,  4   c ,  4   d , the measurement signals S 1 , S 2 , S 3 , S 4  and/or the measured forces. 
     The parameters Mz, Fx, Fy to be determined are thereby the solution to a system of equations, wherein an equation as follows applies to each measurement signal: 
     
       
         
           
             
               S 
                
               
                   
               
                
               1 
             
             = 
             
               
                 
                   a 
                   11 
                 
                 · 
                 Mz 
               
               + 
               
                 
                   a 
                   12 
                 
                 · 
                 Fx 
               
               + 
               
                 
                   a 
                   13 
                 
                 · 
                 Fy 
               
             
           
         
       
       
         
           
             
               S 
                
               
                   
               
                
               2 
             
             = 
             
               
                 
                   a 
                   21 
                 
                 · 
                 Mz 
               
               + 
               
                 
                   a 
                   22 
                 
                 · 
                 Fx 
               
               + 
               
                 
                   a 
                   13 
                 
                 · 
                 Fy 
               
             
           
         
       
       
         
           
             
               S 
                
               
                   
               
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               3 
             
             = 
             
               
                 
                   a 
                   31 
                 
                 · 
                 Mz 
               
               + 
               
                 
                   a 
                   32 
                 
                 · 
                 Fx 
               
               + 
               
                 
                   a 
                   23 
                 
                 · 
                 Fy 
               
             
           
         
       
       
         
           ⋮ 
         
       
       
         
           
             SN 
             = 
             
               
                 a 
                 
                   N 
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                   1 
                 
               
               · 
               Mz 
             
           
         
       
     
     Each coefficient a thereby depends on multiple factors such as, for example, the respective position of the sensor and the orientation of the preferred direction V a , V b , V c , V d  in the reference system, a sensitivity of the respective piezoelement  4   a ,  4   b ,  4   c ,  4   d , and a potential signal loss due to a force shunt from fixing means. 
     Solving such a system of equations for the torque component Mz, a first transverse force component Fx and a second transverse force component Fy requires measurement signals from at least three piezoelements  4   a ,  4   b ,  4   c , with preferred directions V a , V b , V c  oriented so as to lie in a single plane. Moreover, at least two of the preferred directions V a , V b , V c  may not be in either parallel or antiparallel orientation. 
     For this general case described by N=3; i.e. with three piezoelements  4   a ,  4   b ,  4   c , the solution to the above-depicted system of equations is unique. Should further piezoelements be added to the measuring system  1 , the system of equations having three parameters Mz, Fx, Fy to be determined is overdetermined, although the measuring accuracy can be further improved. 
     In the case of N=4, four different systems of equations F (S 1 , S 2 , S 3 ), F (S 1 , S 2 , S 4 ), F (S 1 , S 3 , S 4 ), F (S 2 , S 3 , S 4 ) can be established. The values determined for the individual parameters Mz, Fx, Fy to be determined can then be totaled and averaged; i.e. divided by four in the case of four piezoelements  4   a ,  4   b ,  4   c ,  4   d . Similarly, an overdetermined system of equations F (S 1 , S 2 , . . . , SN), which is solved by means of a minimization task, can be established. 
     If a general solution to the system of equations has been found, calculation of the components Fx, Fy, Mz to be determined can be reduced to matrix multiplication. Same has three rows and as many columns as available measuring signals S 1 , S 2 , S 3 , . . . SN. The matrix elements or coefficients respectively represent the respective contributions of the individual sensors to the parameters Fx, Fy, Mz to be determined. 
     
       
         
           
             
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                         31 
                       
                     
                     
                       
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                         32 
                       
                     
                     
                       
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     Decomposing the measurement signals S 1 , S 2 , S 3 , S 4  into components contributing to the respective parameters Mz, Fx, Fy to be determined requires knowing the position of the piezoelements  4   a ,  4   b ,  4   c  and the orientation of the preferred directions V a , V b , V c , V d . 
     The geometric parameters can be determined either from a design drawing of a measuring system  1  or from knowledge of the preferred directions of the piezoelements  4   a ,  4   b ,  4   d.    
     The orientation of preferred directions V a , V b , V c , V d  of piezoelements  4   a ,  4   b ,  4   c ,  4   d  can however also be determined by determining the preferred directions V a , V b , V c , V d  by way of calibration measurement. Preferably, the measuring system  1  is to that end fixed between two flat plates. In a next step, external transverse forces with a known direction are applied. The preferred direction V a , V b , V c , V d  of piezoelements  4   a ,  4   b ,  4   c ,  4   d  in the plane spanned by the preferred direction V a , V b , V c , V d  of the piezoelements  4   a ,  4   b ,  4   c ,  4   d  can be determined from the magnitude of the individual measurement signals S 1 , S 2 , S 3 , S 4  relative to the magnitude and direction of the transverse forces introduced. 
     Similarly, by applying a defined torque Mz and measuring the individual measurement signals S 1 , S 2 , S 3 , S 4 , a respective distance r a , r b , r c , r d  of the piezoelements  4   a ,  4   b ,  4   c ,  4   d  from a rotational axis D can be determined when the preferred directions V a , V b , V c , V d  of the individual piezoelements  4   a ,  4   b ,  4   c ,  4   d  are known. 
     The described exemplary embodiments are merely examples which are in no way to be limiting of protective scope, application and configuration. Rather, the preceding description affords one skilled in the art a guideline for the implementation of at least one exemplary embodiment, whereby various modifications can be made, in particular with regard to the function and arrangement of the described components, without departing from the protective scope as results from the claims and equivalent combinations of features. In particular, individual exemplary embodiments can be combined with each other. 
     LIST OF REFERENCE NUMERALS 
     measuring system  1   
     bearing apparatus/motor  2   
     shaft  3   
     piezoelement  4   a ,  4   b ,  4   c ,  4   d ,  4   e ,  4   f    
     fixing device  5 ,  5   a ,  5   b ,  5   c ,  5   d    
     coupling  6   a ,  6   b    
     signal processing device  7   
     housing  8   
     measuring arrangement  9   
     supporting apparatus  10   
     opening  11   
     cavity  12   
     gearbox and differential  13   
     wheel dynamometer  14   a ,  14   b    
     test bench  15   
     fixing means  16   a ,  16   b ,  16   c ,  16   d    
     first end face  17   a ,  17   b ,  17   c ,  17   d    
     piezoelement pair  18   a ,  18   b    
     angular sector  19   a ,  19   b ,  19   c    
     second end face  20   b ,  20   d    
     bore  21   a ,  21   b ,  21   c ,  21   d    
     charge dissipator/electrical line  22 ,  22   a ,  22   b ,  22   c ,  22   d    
     preferred direction V a , V b , V c , V d    
     measurement signal S 1 , S 2 , S 3 , S 4   
     rotational axis D