INDUCTIVE SENSOR WITH OPTIMIZED FOOTPRINT

The inductive sensor addresses sensitivity, stroke, and precision issues by using wider receiving coils with optimized spirals and compensation loops, achieving improved accuracy and reduced interference in compact designs.

FR3151090B1Active Publication Date: 2025-07-11MOVING MAGNET TECH
View PDF 0 Cites 0 Cited by

Patent Information

Application Number
FR2023007402
Authority / Receiving Office
FR · FR
Patent Type
Patents
Current Assignee / Owner
Filing Date
2023-07-11
Publication Date
2025-07-11
Estimated Expiration
2043-07-11

AI Technical Summary

Technical Problem

Inductive sensors face limitations in sensitivity, stroke length, and precision due to space constraints, manufacturing irregularities, and interference from parasitic signals, which are exacerbated when higher accuracy is required.

Method used

The sensor design features receiving coils with a width greater than the transmitting coil, optimized spiral patterns, and optional compensation loops to minimize offset voltage and improve signal quality, allowing for compact size and enhanced sensitivity.

Benefits of technology

The design enhances sensitivity, precision, and reduces interference, enabling accurate position detection within constrained spaces while maintaining robustness and reliability.

✦ Generated by Eureka AI based on patent content.

Smart Images

  • Figure 00000014_0000
    Figure 00000014_0000
  • Figure 00000014_0001
    Figure 00000014_0001
  • Figure 00000015_0000
    Figure 00000015_0000
Patent Text Reader

Abstract

The present invention relates to an inductive position sensor for detecting the position of an electrically conductive target, movable above a printed circuit. An oscillator circuit induces an alternating voltage in at least two receiver coils via a transmitter coil. Figure 1
Need to check novelty before this filing date? Find Prior Art

Description

Title of the invention: INDUCTIVE SENSOR WITH OPTIMIZED SPACE REQUIREMENT Field of invention

[0001] The present invention relates to an inductive position sensor for detecting the position of an electrically conductive target, movable above a printed circuit. An oscillator circuit induces an alternating voltage in at least two receiver coils via a transmitter coil.

[0002] The conductive target is driven by the organ whose position is desired to be known and the energy of the transmitting coil(s) induces eddy currents in the target, which in turn generate a magnetic field which is returned and received by the receiving coils.

[0003] Such sensors use the principle of mutual inductance whereby one or more transmitting windings supplied with an alternating signal to generate an alternating magnetic field and receiving windings are arranged to couple. The amount of coupling varies as the displacement of a passive inductive target varies relative to the windings.

[0004] Inductive sensors offer some design flexibility with respect to coil design and are alternatives to magneto-sensitive sensors using, for example, a permanent magnet and a Hall probe.

[0005] Indeed, they allow a wide variety of coil patterns to ensure a variable periodicity making it possible to adapt the measuring range of the sensor and optimize the stroke and precision of the latter, the main limitation comes from the space constraints required in relation to the stroke to be measured.

[0006] The basic principle of inductive sensors is known and has been advantageously used to produce robust and reliable printed circuit board based detectors in hostile environments and in particular in the automotive field. However, small imperfections in the windings and their arrangement lead to imperfections or disturbances in the electromagnetic coupling which, in turn, leads to imperfections or non-linearities in the measurement. Such disturbances or non-linearities come from various sources, including manufacturing irregularities in the windings, capacitive coupling between the windings, crosstalk between the windings, vias between the layers, etc.Such disturbances are inconsequential for relatively low-performance detectors requiring an accuracy of the order of 1% of the travel, but when better accuracies are required, they are problematic, notably because . that imperfections are generally small and numerous, which makes them difficult to eliminate by simple calibration. On the other hand, these sensors require generous transmitting and receiving winding surfaces in order to generate usable electrical signal amplitudes. This results in dimensions that are sometimes incompatible with the constraints of installing the said sensor in its environment. State of the art

[0007] Patent EP3221667B1 is known in the state of the art, describing an inductive position detector comprising a first and a second body, at least one of the bodies being able to move relative to the other along a measurement path, the first body comprising one or more antenna windings which form a first arrangement of windings and the second body comprising a passive resonant circuit which incorporates one or more target windings connected in series with a capacitor.The circuit at least partially covering the first arrangement is characterized in that the first body comprises an additional winding arrangement arranged along at least a portion of the measurement path, the additional winding arrangement being spaced from the first winding arrangement; and in that the second body comprises an additional winding arrangement at least partially covering the additional winding arrangement of the first body.

[0008] Patent application WO2021239175A1 describes a position sensor for detecting the position of an electrically conductive target, comprising at least one transmitter coil, at least one first receiver coil and one second receiver coil and a control device, wherein at least one transmitter coil and the first receiver coil and the second receiver coil are configured and arranged in such a way that an alternating voltage is induced in the first receiver coil via the control device by means of the transmitter coil and can be induced in the second receiver coil, and wherein the transmitter coil and the first receiver coil and the second receiver coil are each arranged as a conductive track structure extending in a plane on a common printed circuit board. The transmitter coil surrounds the first receiver coil and the second receiver coil.The first receiver coil and the second receiver coil have a structure of conductive tracks nested within each other for detecting a position of an electrically conductive target.

[0009] Patent EP351448 IB 1 describes an inductive angular position sensor comprising at least three sensor elements formed of at least one transmitting sensor element and at least two receiving sensor elements, or at least two elements transmitting sensors and at least one receiving sensor element, for measuring the magnetic flux coupling between the transmitting sensor element(s) and the receiving sensor element(s): - a target configured for use with the angular position sensor to detect a rotational position of the target comprising at least two elongated conductive loop structures which are formed by at least two pits or slots in parallel arrangement, to allow eddy currents to flow therein, and configured to affect a magnetic field received from the angular position sensor in a preferential direction along the at least two elongated conductive loop structures, the at least two elongated conductive loop structures being conductively coupled to form discrete electrically conductive paths, and the at least two elongated conductive loop structures being spatially separated; - means for processing signals which are delivered by the at least one receiver sensor element and for delivering at least one signal representative of the angular position of the target. Disadvantages of the prior art

[0010] The solutions of the prior art have several drawbacks.

[0011] In the solutions of the prior art, and in particular in the solution proposed by application WO2021239175, the receiver coils are surrounded by the conductive track forming the transmitter coil. For a given dimension of the printed circuit, the dimension of the receiver coils is limited by this positioning inside the transmitter coil, which has the effect of reducing the sensitivity of the receiver coils.

[0012] Secondly, the useful stroke is limited in relation to the size due to a non-linearity due to the superposition of the winding sections, necessary for closing the receiving coils at the end of the printed circuit.

[0013] Thirdly, configurations providing interlaced coils require high precision of the curved lines formed on the PCB and multiply the number of connecting vias crossing the printed circuit, which introduces local disturbances. In other words, for a given size in the measurement direction, the sensor has the disadvantage of low sensitivity on the one hand and that of a truncated stroke and reduced precision on the other hand.

[0014] Another disadvantage of the known solutions is the relatively low level of the induced signals detected by the receiving coils, which makes these sensors relatively sensitive to interference by parasitic signals of the electronic noise type. Solution provided by the invention

[0015] In order to address these drawbacks, the present invention relates, in its most general sense, to an inductive sensor for determining the angular or linear position of a mobile element comprising: • at least one target made of an electrically conductive material connected to the mobile element along a linear or rotary movement path or a combination of both, • and a circuit consisting of an arrangement of at least one transmitting coil and at least two receiving coils, etched on a printed circuit which may have several layers, the inductive circuit comprising: a. a single transmitting coil formed by a conductive spiral track composed of at least one winding, occupying an area of width Ie, measured perpendicular to the trajectory of movement of the target, b. at least two nested receiving coils each formed by at least one conductive spiral track composed of at least one winding, at least one of said receiving coils occupying a surface of width Ir measured perpendicular to the trajectory of movement of the target, • the spiral tracks each consisting of a multiplicity of longitudinal sections extending along the path of movement and being connected by transverse sections, • said angular or linear position being obtained by the combination of the signals from said receiving coils characterized in that • the width Ir of the surface occupied by at least one of said two receiving coils is greater than or equal to said width hd of the surface occupied by said transmitting coil.

[0016] According to advantageous variants:

[0017] - said longitudinal sections are rectilinear and parallel to the trajectory of displacement, and said transverse sections are rectilinear and parallel to each other, said sensor detecting a linear position.

[0018] - said longitudinal sections are arched and parallel to the trajectory of displacement, and said transverse sections are radial, said sensor detecting an angular position.

[0019] - said first receiving coil has a single spiral.

[0020] - said first receiving coil has a single spiral with variable pitch consisting of a conductive track forming turns generally printed on the same layer of the printed circuit.

[0021] - the distribution of the transverse sections of said first receiving coil does not follow not a cosine law as a function of the distance from the median transverse axis of symmetry of the receiving coil but is optimized to linearize said angular or linear position signal.

[0022] - the distribution of the transverse sections of said first receiving coil are symmetrical with respect to said median transverse axis of symmetry x located at the center of the receiving coil.

[0023] - the distribution of the transverse sections of said second receiving coil does not follow not a sinusoidal law as a function of the distance from the median transverse axis of symmetry of the receiving coil but is optimized to linearize said angular or linear position signal.

[0024] - the distribution of the transverse sections of said second receiving coil are symmetrical with respect to said median transverse axis of symmetry.

[0025] - the sensor further comprises two compensation loops formed of two spirals arranged symmetrically with respect to the transmitting coil, and electrically connected in series with the receiving coil.

[0026] The invention also relates to the association of two periodic angular sensors mentioned above, characterized in that the number of lobes of the two sensors does not have a common integer divisor.

[0027] Detailed description of a non-limiting example of embodiment

[0028] The present invention will be described in more detail with reference to non-limiting examples of embodiment specifying the above-mentioned advantages and considerations. They refer to the appended drawings where:

[0029] [Fig-1] [Fig.l] represents a sectional view of a sensor according to the invention;

[0030] [Fig.2] [Fig.2] represents a view of the configuration of the transmitter coil and a receiving coil corresponding to a first phase, the printed circuit being represented in transparency;

[0031] [Fig.3] [Fig.3] represents a view of the configuration of the transmitter coil and a receiving coil corresponding to a second phase, the printed circuit being represented in transparency;

[0032] [Fig.4] [Fig.4] shows an overview of the coil configuration transmitter, the two receiver coils and the moving target, the printed circuit being shown in transparency;

[0033] [Fig.5] [Fig.5] shows an overview of the coil configuration transmitter with lateral compensation loops;

[0034] [Fig.6] [Fig.6] shows an overview of the coil configuration transmitter with a central compensation loop;

[0035] [Fig.7] [Fig.7] represents an overall view of a sensor according to the invention in a rotating embodiment;

[0036] [Fig.8] [Fig.8] represents the integration of two sensors according to the invention for make a torque sensor;

[0037] [Fig.9] [Fig.9] represents a perspective view of the integration of two sensors according to the invention for producing a torque sensor. General principles of the invention

[0038] [Fig.l] is a sectional view of an inductive sensor. Inductive sensors are generally made up of two components that are movable relative to each other: a. A target (20) which is formed by a conductive part, linked to a movable member, the movement of this part being guided to define a linear or rotary trajectory. This target can be made up of a metal part or a printed circuit comprising a track forming a closed loop b. A multi-layer printed circuit (10) having multiple conductive tracks located at layers (11, 12, 13) of different depth and defining: a. A transmitter coil, powered by an alternating voltage, typically at a frequency of several MHz, formed by conductive tracks printed on at least one of the layers (11) of the printed circuit, b. At least two receiving coils, having spirals of non-constant width, connected to a detection circuit measuring the voltage induced in each of the coils, formed by conductive tracks printed on the faces of the two other layers (12, 13), with through vias for connection with connection tracks.

[0039] Depending on the position of the conductive target (20) relative to these coils formed on the printed circuit (10), the magnetic field induced in the two receiving coils varies due to the modification of the coupling between the transmitting coil and the receiving coils, and the analysis of the voltages induced respectively in each of the coils makes it possible to determine the position of the target (20) as a function of the profile of the spirals and / or the variations in the width of the turns.

[0040] This variation is determined, in certain solutions of the prior art, by the shape of the receiving turns, for example in the shape of an “8”. In other solutions, as well as in the solution which is the subject of the present invention, the variation results from the non-constancy of the pitch of each of the spirals, measured according to the trajectory of the target.

[0041] Configuration of the multi-track printed circuit of the invention

[0042] The printed circuit (10) has several layers (11, 12, 13), on which are printed the conductive tracks defining: a. a transmitter coil (100), b. at least one first receiver coil (200) having a single spiral-shaped lobe, c. at least one second receiver coil (300) having two spiral-shaped lobes, [Fig.l] represents a possible distribution of these coils (100, 200, 300) on the different layers (11, 12, 13) without it being limiting of the invention.

[0043] Optionally, other receiving coils can be provided: a. A third receiving coil to provide a third phase b. And / or redundancy of the receiving coils (200, 300), by doubling them to increase robustness and reliability.

[0044] Optionally, the sensor further comprises one or more compensation coils (400).

[0045] The invention differs from the solutions of the prior art mainly by the fact that the width of the transmitting coil (100) is less than the width of at least one of the receiving coils (200, 300), which makes it possible to minimize the offset voltage in the two receiving loops (200, 300). Indeed, when the receiving coil (200, 300) "extends" laterally from the transmitting coil (100), - the magnetic flux generated by the electric coil crosses the surface of the receiving loop (200, 300) located inside the surface of the transmitting coil (100) in one direction, - and this magnetic flux crosses the surface of the receiving loop (200, 300) located outside the surface of the transmitting coil (100) in the other direction, which creates at least partial compensation, reducing the voltage induced in the secondary loop (200, 300) and avoids the need for electronic offset compensation.

[0046] Conventional electronic components sometimes provide an offset compensation function, but limited to levels lower than the voltage induced in the receiving loops of prior art sensors. Linear implementation variant

[0047] The transmitter coil (100) is formed by a conductive track printed on an insulating layer of the printed circuit (10) and forming a spiral track (110) with a constant pitch, an output track being provided on the opposite face of the layer for connecting the inner end of the spiral.

[0048] For a linear sensor, this spiral track (110) has the shape of a rectangular spiral with rectilinear transverse sections (116, 117, 118, 119) alternating with longitudinal sections (111, 112, 113, 114) also rectilinear and parallel to the axis of the movement path (25) of the target (20) relative to the printed circuit (10).

[0049] The two receiving coils (200, 300), visible in [Fig.2] and 3, are formed on layers distinct from that on which the transmitting coil (100) is printed.

[0050] These two receiving coils (200, 300) are nested, that is to say that they are neither totally included in one another, nor totally offset from one another. The longitudinal surfaces defined by each of the receiving coils (200, 300) have an overlapping zone when viewed from a direction orthogonal to the transverse plane.

[0051] Each of the receiving coils (200, 300) has the shape of a spiral with preferably rectangular turns.

[0052] The first receiving coil (200) has a single spiral track (210) with rectilinear transverse sections (216, 217, 218) alternating with longitudinal sections (211, 212, 213) also rectilinear and parallel to the axis of the movement path (25) of the target (20) relative to the printed circuit (10). The parallel transverse sections (216, 217, 218) have a variable distance between them to form a variable pitch coil formed by a conductive track forming turns generally printed on the same layer of the printed circuit.

[0053] Unlike the prior art, the variation in pitch between two transverse sections of the first receiving coil (200) does not follow a strictly sinusoidal law, but a distribution optimized as a function of the shape of the target (20) and the length available in the direction of the movement path. This singular distribution is inherent in the production of the first receiving coil (200) in a single spiral track (210) compared to three for the prior art. This production in a single spiral track (210) not only provides a simplification of the connection and production, but also to obtain a more compact receiving coil (200) making it possible to minimize the size of the printed circuit for equivalent performance.

[0054] The distance between two consecutive receiving turns varies by increasing or decreasing on either side of a transverse axis (30) up to the outer turn. The transverse axis (30) being centered on the transmitting coil and perpendicular to the trajectory (25).

[0055] The second receiving coil (300) has two conductive tracks forming spiral tracks (310, 320) whose transverse sections are symmetrical with respect to the transverse axis (30), perpendicular to the axis of the movement path (25) of the target (20). These two spiral tracks (310, 320) are connected in series to form a single coil. For each spiral track (310, 320), the pitch of the transverse sections varies upwards or downwards from the transverse axis (30).

[0056] These conductive spiral tracks (310, 320) are generally printed on the same layer of the printed circuit, but a different layer from that on which the first receiving coil (200) is printed.

[0057] Note that the transverse sections of the coils (100, 200, 300) have been represented in a rectilinear manner and parallel to each other. It should be noted that this representation is in no way limiting of the invention but simply illustrates the simplest form to optimize numerically, these sections could be oblique to each other, or even undulate, as long as it is possible to obtain a distribution allowing a linear variation of the position signal from the sensor as a function of the position of the target and this throughout the movement trajectory (25). The same remark is valid for the longitudinal sections.

[0058] Relative dimensioning of the transmitter coils (100) and receiver coils (200, 300)

[0059] As visible in figure 4, according to a transverse orientation of the printed circuit, the transmitter coil(s) (100) are inscribed in a shape of width h: and length LE and the receiver coils (200, 300) are inscribed in a shape of width Ir and length LR

[0060] In order to compensate for the offsets and improve the precision and quality of the detected signals, the width Ie of the transmitting coil (100) is less than the width Ir of at least one of the receiving coils (200, 300).

[0061] It is preferable that the single-lobe receiver coil (200) is wider than the transmitter coil (100) in order to minimize the offset induced across this coil.

[0062] Preferably, the width of each of the spiral tracks (210, 310, 320) of each of the receiving coils (200, 300) is greater than the width of the transmitting coil (100).

[0063] On the other hand, the length measured along the linear or arcuate trajectory of the target of the single-lobe (200) and double-lobe (300) receiver coils is between 0.8 x Le and 1 x Le and preferably greater than 0.9 x LE.

[0064] The receiver coil (200) is formed by a single lobe, and not by three complementary lobes, even in cases where a second coil (200) is provided to create redundancy. Rotary production variant

[0065] All the characteristics set out for the linear variant are also present for a rotary embodiment, such as that presented in [Fig.7]. Nevertheless, the displacement path (25) of the target (20) relative to the printed circuit is not rectilinear, but arcuate, the longitudinal sections (111, 211, 311, 321) of the tracks spirals (110, 210, 310, 320) are not rectilinear but arcuate, and the transverse sections (116, 216, 316, 326) are arranged substantially along radii.

[0066] The lengths LE and L^ of the partially discal shapes, inscribing the transmitting coil on the one hand and the receiving coils on the other hand, are angular lengths preserving the relationships stated for the linear case. Compensation loops (400)

[0067] [Fig. 5] and 6 illustrate alternative embodiments of a sensor comprising compensation loops (400, 401, 403). In addition, the embodiment of [Fig. 5] has two compensation loops (400, 401). These compensation loops (400, 401) are formed of two spirals arranged symmetrically with respect to the transmitter coil (100), and electrically connected in series with the receiver coil (200).

[0068] These compensation loops (400, 401) can be arranged laterally, in the area between the external turn of the transmitter coil (100) and the receiver coil (200).

[0069] It may also be noted that a single compensation loop (403) housed in the center of the transmitter coil may also be used, as shown in [Fig.6].

[0070] The function of these compensation coils is to recover a flux opposing the main flux induced by the transmitter coil (100), without being affected by the position of the target (25). Signal processing

[0071] The receiving coils (200, 300) deliver two alternating signals, with a frequency corresponding to the frequency of the transmitting coil (100), and an amplitude varying as a function of the flux passing through the receiving coils (200, 300) due to the coupling with the target (20), and therefore the position of the target (20). A processor processes these two alternating signals to extract the position information therefrom. Preferably, the transverse sections of the receiving coils (200, 300) are distributed so that the latter provide, as a function of the position of the target, signals describing sinusoids in phase quadrature, the absolute position is then obtained by calculating the arctangent of the ratio of these signals.However, this is not limiting of the invention and the distribution of the transverse sections of one, the other or both receiving coils (200, 300) can be optimized, in order, after post-processing and combination of the signals from the receiving coils, to obtain the absolute position of the target (20). The signals are filtered to eliminate the signals whose frequency is different from the supply frequency of the transmitting coil (100), in order to ensure high resistance to disturbing magnetic fields.

[0072] The useful travel of the target (20) is close to the length LR of the longest of the receiving coils (200, 300), which makes it possible to optimize the size of the sensor and the multilayer circuit.

[0073] For certain applications, the multilayer circuit is produced in the form of a flexible circuit, to allow winding around a three-dimensional organ whose position is desired to be known.

[0074] The multi-layer circuit may be overmolded to provide moisture resistance. Integration with a torque sensor

[0075] [Fig. 8] illustrates an example of use of an inductive sensor according to the invention for producing a torque sensor, typically measuring the torsion of a steering column shaft or a bicycle crankset. Torque sensors must be able to measure small angular variations, typically a few tenths of a degree to a few degrees, and this for a shaft potentially in continuous rotation. The torque measurement can be done in a known manner by measuring an angle difference at the two ends of a shaft whose mechanical properties of elastic deformation in torsion are known. It is then entirely appropriate to use two sets of rotating inductive sensors (500, 600) according to the invention, as shown in [Fig.8], to measure the angle at each end of the torsion shaft, the receiver coils of the two sets being fixed relative to each other and the targets (520, 620) being each connected to the torsion shaft (not shown). The rotary inductive sensor sets nevertheless differ from the embodiment shown in [Fig.7] in that they are optimized for a reduced angular travel, thus the target travels the entire pattern in an angle variation of less than 60°, thus obtaining a reduction in the measured angle compared to the mechanical angle achieved. In order to optimize the sensitivity of the measured signal, it is possible to angularly repeat the number of coils by connecting them electrically in series and the targets (520, 620) by connecting them mechanically. This gives a flower pattern with six petals visible in [Fig.8].In order to limit the influence of one sensor on the other, the two sensors can have a different number of lobes, and more particularly the number of lobes of each of the sensors must not have a common integer divisor, we then speak of an Asian configuration.

Claims

1. Claims - Inductive sensor for determining the angular or linear position of a moving element comprising: • at least one target (20) made of an electrically conductive material connected to the mobile element along a linear, rotary movement path (25) or a combination of both, • and a circuit consisting of an arrangement of at least one transmitting coil (100) and at least two receiving coils (200, 300) comprising a first receiving coil (200) and a second receiving coil (300), etched on a printed circuit which may have several layers (10), the inductive circuit comprising: a. a single transmitting coil (100) formed by a conductive spiral track (110) composed of at least one winding, occupying a surface of width h, measured perpendicular to the movement path (25) of the target (20), b. at least two nested receiving coils (200, 300) each formed by at least one conductive spiral track (210, 310) composed of at least one winding, at least one of said receiving coils (200, 300) occupying a surface of width Ir measured perpendicular to the movement path (25) of the target (20), the spiral tracks (110, 210, 310) each consisting of a multiplicity of longitudinal sections (111, 211, 311, 321) extending along the movement path and being connected by transverse sections (116, 216, 316, 326), said angular or linear position being obtained by the combination of the signals from said receiving coils (200, 300) characterized in that the width Ir of the surface occupied by at least one of said two receiving coils (200, 300) is greater than or equal to said width ^ of the surface occupied by said transmitting coil (100).

2. - Inductive sensor according to claim 1 characterized in that said longitudinal sections (111, 211, 311, 321) are rectilinear and parallel to the movement path (25), and said transverse sections (116, 216, 316, 326) are rectilinear and parallel to each other, said sensor detecting a linear position.

3. - Inductive sensor according to claim 1 characterized in that said longitudinal sections (111, 211, 311, 321) are arcuate and parallel to the movement path (25), and said transverse sections (116, 216, 316, 326) are radial, said sensor detecting an angular position.

4. - Inductive sensor according to any one of the preceding claims characterized in that said first receiving coil (200) has a single spiral.

5. - Inductive sensor according to the preceding claim characterized in that said first receiving coil (200) has a single spiral with variable pitch constituted by a conductive track forming turns generally printed on the same layer of the printed circuit.

6. - Inductive sensor according to the preceding claim characterized in that the distribution of the transverse sections (216, 217, 218) of said first receiving coil (200) are symmetrical with respect to said median transverse axis of symmetry (30) located at the center of the receiving coil (200). 7- Inductive sensor according to the preceding claim characterized in that the distribution of the transverse sections (316, 317, 326, 327) of said second receiving coil (300) are symmetrical with respect to said median transverse axis of symmetry (30).

8. - Inductive sensor according to claim 1 characterized in that it further comprises two compensation loops (400, 401) formed of two spirals arranged symmetrically with respect to the transmitting coil (100), and electrically connected in series with said first receiving coil (200).

9. - Association of two periodic angular sensors according to claim 1 characterized in that the number of lobes of the two sensors does not have a common integer divisor.