HP Record ID 85867771 DETECTION OF TONER DENSITY USING A THREE-DIMENSIONAL MAGNETIC SENSOR BACKGROUND [0001] Some image forming apparatuses use a sensor such as a magnetic permeability sensor or an optical sensor to detect a toner density of developer, in order to maintain the toner density constant, for better quality in the image formed. BRIEF DESCRIPTION OF THE DRAWINGS [0002] Fig. 1 is a schematic diagram showing an example image forming apparatus. Fig. 2 is a transverse cross-sectional view of an example developing device having a three-dimensional magnetic sensor according to an example. Fig. 3 is a top plan view of components of the example developing device illustrated in Fig.2. Fig. 4A is a partial top plan view of a stirring and conveyance device of an example developing device including a magnet attached to the stirring and conveyance device. Fig.4B is a cross-sectional view of the stirring and conveyance device of Fig.4A, taken along the line A-A. Fig.4C is a partial enlarged view of the stirring and conveyance device illustrated 1 in Fig. 4B, illustrating the magnet.

Fig. 5 is a graph illustrating a correlation between toner densities and peak values of a magnetic flux density generated by the magnet illustrated in Fig. 4A. Fig. 6 is a graph of magnetic flux densities detected during one rotation of the stirring and conveyance device illustrated in Fig. 4A.

Fig. 7A is a partial top plan view of a stirring and conveyance device of an example developing device including a magnet attached to the stirring and conveyance device.

Fig. 7B is a cross-sectional view of the stirring and conveyance device of Fig. 7A, taken along the line B-B.

Fig. 7C is a partial enlarged view of the stirring and conveyance device illustrated In Fig. 7B, illustrating the magnet.

Fig. 8 is a graph illustrating a correlation between toner densities and peak values of a magnetic flux density generated by the magnet illustrated in Fig. 7 A. Fig. 9 is a graph of magnetic flux densities detected during one rotation of the stirring and conveyance device illustrated in Fig. 7A.

Fig. 10A is a partial top plan view of a stirring and conveyance device of an example developing device including a magnet attached to the stirring and conveyance device.

Fig. 10B is a cross-sectional view of the stirring and conveyance device of Fig. 10A. taken along the line C-C.

Fig. 10C is a partial enlarged view of the stirring and conveyance device illustrated in Fig. 10B, illustrating the magnet.

Fig. 11 is a graph illustrating a correlation between toner densities and peak values of a magnetic flux density generated by the magnet illustrated in Fig. 10A. Fig. 12 is a graph of magnetic flux densities detected during one rotation of the stirring and conveyance device illustrated in Fig. 10A.

Fig. 13 is a transverse cross-sectional view of an example developing device having a three-dimensional magnetic sensor according to an example.

Fig. 14 is a transverse cross-sectional view of an example developing device having a three-dimensional magnetic sensor according to an example.

Fig. 15 is a graph illustrating a correlation between toner densities and magnetic flux densities in the example developing device illustrated in Fig. 14.

Fig. 18 is a schematic diagram of an example storage device.

DETAILED DESCRIPTION

[0003] In the following description, with reference to the drawings, the same reference numbers are assigned to the same components or to similar components having the same function, and overlapping description is omitted. [0004] Fig. 1 illustrates an example image forming apparatus 1. The example image forming apparatus 1 includes for each of four toner colors of magenta, yellow, cyan and black, a toner bottle N, a developing device 20, a photosensitive drum 40, a charging roller 41 and a cleaning unit 43. Accordingly, the image forming apparatus 1 includes four toner bottles N, four developing devices 20, four photosensitive drum 40, four charging rollers 41 and four cleaning units 43, associated with the four colors of toner. The example image forming apparatus 1 includes a recording medium conveyance unit 70, a transfer device 30, an exposure unit 42, a fixing device 50 and a discharge device 60 The transfer device 30 includes an intermediate transfer belt 31, support rollers 34, 35, 36, 37 to support the intermediate transfer belt 31 in a circularly movable manner, four primary transfer rollers 32 corresponding to the four photosensitive drums 40, respectively, and a secondary transfer roller 33 that are rotatable to following the movement of the intermediate transfer belt 31 while pressing a paper sheet P against the intermediate transfer belt 31. The support roller 37 is a driving roller for circularly driving the intermediate transfer belt 31 in a direction indicated by the arrows. The example image forming apparatus 1 includes a processor 80 to control the operation of various constituent elements of the image forming apparatus 1 , and a memory 82 to store various control instructions to be executed by the processor 80 or relevant data. The processor 80 may be a controller 80

[0005] Each of the charging rollers 41 charges the corresponding one of the photosensitive drums 40and the exposure unit 42 forms an electrostatic latent image on the photosensitive drum in accordance with image data of the corresponding toner color. Thereafter, the electrostatic latent image is developed by a corresponding one of the developing devices 20, with toner from a corresponding one of the toner bottles N, thereby forming a toner image.

Toner images of the four colors formed on the respective four photosensitive drums 40 are layered on the intermediate transfer belt 31 in a sequential order by the primary transfer roller 31 to be combined into a single composite toner image. The composite toner image formed on the intermediate transfer belt 31 is then transferred on the paper sheet P by the secondary transfer roller 33, and fixed on the paper sheet P by the fixing device 50 which includes a heating roller

52 and a pressing roller 54. The paper sheet P is conveyed one at a time, by the recording medium conveyance unit 70 from a cassette K along a conveyance path P1 . The secondary transfer roller 33 transfers the composite toner image to HP Record ID 85867771 the paper sheet P, and the discharge device 60 which includes the discharge rollers 62, 64. [0006] Figs. 2 and 3 show an example developing device 100, which can be implemented in the example image forming apparatus 1. The developing device 100 includes a container 101 to store developer, and a first second stirring and conveyance devices 110 and a second stirring and conveyance device 120 that are disposed in the container 101. The developer includes toner and magnetic carrier. [0007] The first stirring and conveyance device 110 conveys, while stirring, the developer in the direction D1, and delivers the developer to the second stirring and conveyance device 120 through an opening 103 of a partition 102. The second stirring and conveyance device 120 conveys, while stirring, the developer in the direction D2 that is opposite to the direction D1, and delivers the developer to the first stirring and conveyance device 110 through an opening 104 of the partition 102. Accordingly, the developer is conveyed circularly within the container 101. [0008] The developing device 100 includes, within the container 101, a developer roller 130 disposed adjacent the first stirring and conveyance device 110, on a side opposite the second stirring and conveyance device 120. The developer roller 130 includes a core 128 (e.g., a core shaft) including a magnet, and a sleeve 129 rotatably disposed around the core 128. The developer roller 130 adsorbs by a magnetic force a portion of developer from the first stirring and conveyance device 110, and supplies the adsorbed developer to the photosensitive drum 40 through an opening 105 of the container 101. [0009] The first stirring and conveya device 110 includes a rotating axis 112 5 and an auger (or screw conveyor) 114 extending around the rotating axis 112. The second stirring and conveyance device 120 includes a rotating axis 122 and an auger (or screw conveyor) 124 extending around the rotating axis 122.

[0010] In order to detect a toner density of the developer contained in the container 101 , the developing device 100 has a magnet 140 and a three-dimensional (3D) magnetic sensor 160. The term "toner density” refers to weight percent concentration of toner in the developer. Even when a one-dimensional magnetic sensor that detects a magnetic flux density component in one direction is used, it can theoretically determine a toner density from the detected magnetic flux density component in the one direction. However, in this case, a slight displacement of position or angle for attachment of a sensor or a magnet can substantially reduce a detected magnetic flux density component, making it more difficult to accurately detect a toner density. According examples, a composite value associated with magnetic flux density components in the x, y and z directions detected by a three-dimensional magnetic sensor is used to determine a toner density, while reducing an influence caused by an error of position or angle for attachment of the magnet 140 and/or the three-dimensional magnetic sensor 160.

[0011] Figs. 4A to 4C illustrate the magnet 140. The auger 124 includes a stirring plate 124a extending linearly along the rotating axis 122, and the magnet

140 is adhered to a surface of the stirring plate 124a with a two-sided adhesive tape. The magnet 140 may be mounted to the stirring plate 124a with an adhesive or other adhesion agent, for example, instead of a two-sided adhesive tape. The magnet 140 may be coupled to the second stirring and conveyance device 120 in such a manner so as to generate a magnetic flux without causing a substantial impact on the stirring or the conveyance of the developer.

[0012] The magnet 140 has opposite ends in a rotating direction of the auger 124. The magnet 140 is a double-sided unipolar magnetized magnet having magnetic poles at the opposite ends in the rotating direction. Magnetic poles of N and S indicated in Fig. 4C may be reversed. The double-sided unipolar magnetized magnet 140 is less likely influenced by an error in the position or angle for attachment of the magnet 140 or the three-dimensional magnetic sensor 160, than a single-sided unipolar magnetized magnet. For example, the magnet 140 having the magnetic poles at the opposite ends in the rotating direction of the auger 124 reduces an attenuation of magnetic flux density, which is caused by a distance from the magnet.

[0013] The three-dimensional magnetic sensor 160 is disposed, as shown in Fig. 2, adjacent the second stirring and conveyance device 120 so as to have a sensing surface 164 within the container 101 , for example to substantially face the second stirring and conveyance device 120. The three-dimensional magnetic sensor 160 is adhered to a base member 162, and fitted into an opening formed in a wall of the container 101. Positioning the sensing surface 164 within the container 101 shortens the distance from the magnet 140 to the sensing surface 164, enabling the toner density to be detected with greater accuracy. In addition, the developer adsorbed by the magnet 140 may clean the sensing surface 164 as the auger 124 rotates, to increase stability of the detection of the magnet flux density. In addition, the three-dimensional magnetic sensor 160 is positioned to face the second stirring and conveyance device 120 to detect the toner density with greater accuracy since the developer is likely to collect around the second stirring and conveyance device 120 which is positioned lower than the first stirring and conveyance device 110. In some examples, as will be described with reference to Fig. 13, the three-dimensional magnetic sensor may be disposed externally to a container 201 .

[0014] The three-dimensional magnetic sensor 160 detects, at a position of the sensor 160, magnetic flux density components in x, y and z directions (e.g., directions along three axes of a three-dimensional Cartesian system that are orthogonal to one another) of a magnetic flux generated by the magnet 140, and outputs to the processor 80, respective signals (for example, voltage signals) indicating the detected magnetic flux density components in the x, y and z directions. An example of such a three-dimensional magnetic sensor to detect magnetic flux density components in the x, y and z directions includes AK09970N commercially available from AKM (Asahi Kasei Microdevices). However, any other suitable three-dimensional magnetic sensor may be used. [0015] The processor 80 calculates a composite value (for example, size of a resultant vector) of the magnetic flux density components in the x, y and z directions detected by the three-dimensional magnetic sensor 160; and based on the composite value, determines a toner density of the developer within the container 101. When the magnetic flux density components in the x, y and z directions are represented by Bx, By and Bz [mT], a composite value B [mT] (hereinafter, referred to as "magnetic flux density") of the magnetic flux density components in the x, y and z directions, is calculated according to the equation B = (Bx ² -rBy ² -i-Bz ² ) ^i/2

[0018] On the assumption that a distance from the magnet 140 to the three-dimensional magnetic sensor 160 is constant, as the toner density of the developer within the container 101 increases, the magnetic flux density (the density of magnetic flux) detected by the three-dimensional magnetic sensor 160 increases. Based on this correlation between the magnetic flux density and the toner density, a magnetic flux density defected by the three-dimensional magnetic sensor 160 allows determination of a toner density of the developer within the container 101. However, in the case in which the magnet 140 is coupled to the auger 124, the distance from the three-dimensional magnetic sensor 160 to the magnet 140 varies periodically as the auger 124 rotates. Accordingly, the toner density within the container 101 cannot be determined simply from the magnetic flux density detected by the three-dimensional magnetic sensor 160. In order to substantially compensate for the variations in the distance, the processor 80 focuses on a "peak value" of the magnetic flux density defected during the rotation of the auger 124 to determine a toner density of the developer within the container 101. The peak value of the magnetic flux density corresponds to a magnetic flux density when the rotating magnet 140 is located at a position closest to the three-dimensional magnetic sensor 160. [0017] Prior to the determination of a toner density, a memory (or storage device) 82 may have stored thereon data indicating a correlation (for example, a correlation as will be described with reference to Figs. 5, 8 and 11) between the peak value of the magnetic flux densities and toner densities measured by using the magnet 140 and the three-dimensional magnetic sensor 160 attached to the developing device 100. This correlation may be measured, for example, at a factory, and stored in the memory 82. However, the three-dimensional magnetic sensor 160 may be influenced by geomagnetism or an ambient temperature, the amount of developer within a toner bottle, etc. Accordingly, the image forming apparatus 1 can calibrate the correlation stored in the memory 82 when the location for installing the image forming apparatus 1 is changed or toner bottles are replaced. The processor 80 carries out the calibration by acquiring outputs from the three-dimensional magnetic sensor 160, for example, in a first state wherein the container 101 contains no developer, and in a second state wherein the container 101 contains developer with a predetermined toner density. It will be appreciated that the calibration may be carried out with other suitable methods.

[0018] Fig. 5 shows an example of a correlation between magnetic flux densities (peak value) and toner densities measured in the developing device 100 including the magnet 140. When the toner densities are in the range of about 0 to 15% as illustrated, the magnetic flux densities (peak value) can be approximated by a linear function. This correlation may be stored in the memory 82 in the form of the linear function, f = ax + b, or in the form of a lookup table. Since the three-dimensional magnetic sensor 160 is associated with a linear correlation between magnetic flux densities (peak value) and toner densities, it can detect a toner density more precisely for a wider range of toner densities as compared with a magnetic permeability sensor having a logarithm property (e.g , a magnetic permeability sensor that is characterized by a logarithmic correlation).

[0019] During an operation of the image forming apparatus 1 , the processor 80, uses the peak value of the magnetic flux density detected by the three-dimensional magnetic sensor 160, for example, during one rotation of the auger 124, to determine a toner density of the developer within the container 101 , based on the correlation read from the memory 82 between magnetic flux densities (peak value) and toner densities. According to examples, the processor 80 takes samples of outputs from the three-dimensional magnetic sensor 180 at constant time intervals during one rotation of the auger 124, and calculates a composite value of magnetic flux density from sampled magnetic flux density components in the x. y and z directions, so that a peak value of the composite value can be determined. In examples where the correlation is stored in the form of a lookup table, the processor 80 may apply an interpolation to the data in the lookup table to determine or interpolate a toner density.

[0020] Fig. 6 shows an example of magnetic flux densities detected by the three-dimensional magnetic sensor 180 during one rotation of the auger 124 in the developing device 100 including the magnet 140. The horizontal axis indicates a relative angle position in degrees (deg), of the magnet 140 around the rotating axis 122. The vertical axis indicates a magnetic flux density (ml) of a magnetic flux detected by the three-dimensional magnetic sensor 160. In this example, the peak value of the detected magnetic flux densities is about 8.5 mT. Thus, the processor 80 can determine, from the correlation shown as the linear function, for example, in Fig. 5, a toner density of about 6.5 weight%. If the determined toner density is outside a predetermined operation range (e.g., a range of suitable operation, for example, of about 6% to 12%), the processor 80 can command (or control) a toner feeding mechanism to adjust the toner density. [0021] In order to improve the detection accuracy of a toner density, the processor 80 may determine a toner density of the developer within the container 101 based on an average value of peak values of magnetic flux densities detected by the three-dimensional magnetic sensor 160 during a plurality of rotations of the auger 124. For example, the processor 80 may determine one peak value for each rotation. [0022] Figs. 7 A to 7C illustrate a magnet 140A according to another example, which can be implemented in the developing device 100. The auger 124 includes a stirring plate 124a extending linearly along the rotating axis 122, and the magnet 140A is adhered to a surface of the stirring plate 124a with a two-sided adhesive tape. The magnet 140A may be mounted to the stirring plate 124a with an adhesive or other adhesion agent, for example, instead of a two-sided adhesive tape. The magnet 140A may be coupled to the second stirring and conveyance device 120, in such a manner, for example, to generate a magnetic flux without causing a substantial impact on stirring or conveyance of developer.

[0023] The magnet 140A has opposite ends in a radial direction of the rotating axis 122 of the auger 124. The magnet 140A is a double-sided unipolar magnetized magnet having magnetic poles at the opposite ends thereof in the radial direction. The magnetic poles of N and S may be reversed in some examples. The double-sided unipolar magnetized magnet 140A is less likely influenced by an error in the position or angle for attachment of the magnet 140A or the three-dimensional magnetic sensor 180, in comparison to a single-sided unipolar magnetized magnet

[0024] Fig. 8 shows an example of a correlation between magnetic flux densities (peak value) and toner densities measured at the developing device

100 including the magnet 140A. When the toner densities are in the range of about 0 to 15% as illustrated, the magnetic flux densities (peak value) can be approximated by a linear function. This correlation may be stored in the memory 82 in the form of the linear function, f = ax + b, or in the form of a lookup table. Since the three-dimensional magnetic sensor 160 provides a linear correlation between magnetic flux densities (peak value) and toner densities, it can detect a toner density more precisely in a wider range of toner densities as compared with a magnetic permeability sensor having a logarithm property [0025] During an operation of the image forming apparatus 1 , the processor 80 uses the peak value of the magnetic flux density detected by the three-dimensional magnetic sensor 160, for example, during one rotation of the auger 124, to determine a toner density of the developer within the container 101 , based on the correlation read from the memory 82 between magnetic flux densities (peak value) and toner densities. According to examples, the processor 80 takes samples of outputs from the three-dimensional magnetic sensor 160 at constant time intervals during one rotation of the auger 124, and calculates a composite value of magnetic flux density from sampled magnetic flux density components in the x, y and z directions, so that a peak value of the composite value can be determined. In examples where the correlation is stored in the form of a lookup table, the processor 80 may apply an interpolation to the data in the lookup table to be able to determine or interpolate a toner density.

[0026] Fig. 9 shows an example of magnetic flux densities detected by the three-dimensional magnetic sensor 160 during one rotation of the auger 124 in the developing device 100 including the magnet 140A. The horizontal axis indicates a relative angle position in degrees (deg) of the magnet 140A around the rotating axis 122. The vertical axis indicates a magnetic flux density (ml) of the magnetic flux detected by the three-dimensional magnetic sensor 160. In this example, the peak value of the detected magnetic flux densities is about

10.4 mT. Thus, the processor 80 can determine a toner density of about 8.0 weighl% from the correlation shown as the linear function, for example in Fig. 8. If the determined toner density is outside a predetermined operation range (e.g., a range of suitable operation, for example about 8% to 12%), the processor 80 can command (or control) a toner feeding mechanism to adjust the toner density. [0027] In order to improve the detection accuracy of a toner density, the processor 80 may determine a toner density of the developer within the container 101 based on an average value of peak values of magnetic flux densities detected by the three-dimensional magnetic sensor 180 during a plurality of rotations of the auger 124. For example, the processor 80 may determine one peak value for each rotation.

[0028] Figs. 10A 10C illustrate a magnet 140B according to another example, which can be implemented in the developing device 100. The auger 124 includes a stirring plate 124a extending linearly along the rotating axis 122, and the magnet 140B is adhered to a surface of the stirring plate 124a with a two-sided adhesive tape. The magnet 140B may be mounted to the stirring plate 124a with an adhesive or other adhesion agent, for example, instead of a two-sided adhesive tape. The magnet 140B may be coupled to the second stirring and conveyance device 120, in such a manner, for example, to generate a magnetic flux without causing a substantial impact on stirring or conveyance of developer.

[0029] The magnet 140B has an end (or front edge) in a rotating direction of the auger 124. The magnet 140B is a single-sided multipolar magnetized magnet having magnetic poles at the end thereof in the rotating direction of the auger

124. The magnet 140B has alternating magnetic poles of and S along a front edge portion in the rotating direction of the auger 124. In other examples, the magnet 140B may have alternating magnetic poles of N and S along a rear edge portion that is opposite the front edge portion in the rotating direction of the auger

124. The single-sided multipolar magnetized magnet 140B reduces the sampling error of the peak value in determining a peak value described below.

[0030] Fig. 11 shows an example of a correlation between magnetic flux densities (peak value) and toner densities measured at the developing device

100 including the magnet 140B. When the toner densities are in the range of about 0 to 15% as illustrated, the magnetic flux densities (peak value) can be approximated by a linear function. This correlation may be stored in the memory 82 in the form of the linear function, f = ax + b, or in the form of a lookup table. Since the three-dimensional magnetic sensor 180 provides a linear correlation between magnetic flux densities (peak value) and toner densities, it can detect a toner density more precisely in a wider range of toner densities as compared with a magnetic permeability sensor having a logarithm property.

[0031] During an operation of the image forming apparatus 1 , the processor 80 uses the peak value of the magnetic flux density detected by the three-dimensional magnetic sensor 180, for example, during one rotation of the auger 124, to determine a toner density of the developer within the container 101 , based on the correlation read from the memory 82 between magnetic flux densities (peak value) and toner densities. According to examples, the processor 80 takes samples of outputs from the three-dimensional magnetic sensor 180 at constant time intervals during one rotation of the auger 124, and calculates a composite value of magnetic flux density from sampled magnetic flux density components in the x, y and z directions, so that a peak value of the composite value can be determined. In examples where the correlation is stored in the form of a lookup table, the processor 80 may apply an interpolation to the data in the lookup table to determine or interpolate a toner density

[0032] Fig. 12 shows an example of magnetic flux densities detected by the three-dimensional magnetic sensor 160 during one rotation of the auger 124 in the developing device 100 having the magnet 140B. The horizontal axis indicates a relative angle position in degrees (deg) of the magnet 140B around the rotating axis 122. The vertical axis indicates a magnetic flux density (mT) of the magnetic flux detected by the three-dimensional magnetic sensor 160. In this example, the peak value of the detected magnetic flux densities is about 3.1 mT. Thus, the processor 80 can determine, from the correlation shown as the linear function, for example, in Fig. 11 , a toner density of about 8.0 weigbt%. If the determined toner density is outside a predetermined operation range (e.g., a range for suitable operation, for example, of about 6% to 12%), the processor 80 can command (or control) a toner feeding mechanism to adjust the toner density. [0033] In order to improve the detection accuracy of a toner density, the processor 80 may determine a toner density of the developer within the container 101 based on an average value of peak values of magnetic flux densities detected by the three-dimensional magnetic sensor 160 during a plurality of rotations of the auger 124. For exampie, the processor 80 may determine one peak value for each rotation

[0034] Fig. 13 shows a developing device 200 according to another example, which can be implemented in the example image forming apparatus 1. The developing device 200 is similar to the developing device 100 (cf. Figs. 2 and 3), with some differences, for example, the developing device 200 has a container

201, and a three-dimensional magnetic sensor 260 is disposed externally to the container 201 to detect magnetic flux density components in the x, y and z directions of magnetic flux generated at a position of the sensor through a wall of the container 201. The three-dimensional magnetic sensor 280 is fixed to an exterior surface of the container 201 by a fixing member 282. The fixing member 282 is fitted into a depression formed on the exterior surface of the container 201. In other examples, the three-dimensional magnetic sensor 260 may be adhered directly to the exterior surface of the container 201 with, for example, a two-sided adhesive tape or an adhesive. Accordingly, the developing device 200 allows for an easy attachment of the three-dimensional magnetic sensor 280. The developing device 200 has a magnet 240, which is similar to the magnet 140 (cf. Fig. 2). In some examples, instead of the magnet

240, the developing device 200 may include the magnet 140A (cf. Fig. 7), or the magnet 140B (cf. Fig. 10) according to other examples. Components of the developing device 200 that correspond substantially to components of the develop device 100 are indicated by a reference number equivalent to "100" added to the reference number of the corresponding component of the developing device 100, and overlapping description is omitted.

[0035] Fig. 14 shows a developing device 300 according to another example, which can be implemented in another image forming apparatus. The developing device 300 is similar to the developing device 100, with some differences. For example, the developing device 300 includes a developer roller

330, a three-dimensional magnetic sensor 360 that is disposed adjacent the developer roller 330, and a magnet 340 that is included in the developer roller

330. In addition, a first stirring and conveyance device 310, a second stirring and conveyance device 320 and the developer roller 330 have rotating directions opposite to those of the corresponding components in the developing device 100 (cf. Fig. 2). Components of the developing device 300 that correspond substantially to components of the develop device 100 are indicated by a reference number equivalent to "200" added to the reference number of the corresponding component of the developing device 100, and overlapping description is omitted

[0038] The developing device 300 includes, within a container 301, the developer roller 330 disposed adjacent to the first stirring and conveyance device 310 The developer roller 330 includes a cylindrical core 328, and a rotatable sleeve 329 disposed around the core 328 The developer roller 330 adsorbs by a magnetic flux a portion of developer from the first stirring and conveyance device 310, and supplies the adsorbed developer to a photosensitive drum 370 through an opening 305 of the container 301. Accordingly, the core 328 includes a plurality of magnets 340 forming, for example, five magnetic poles including for example, a first conveyance pole, a developing pole, a second conveyance pole, a separation pole and a layer regulation pole, located around the core 328.

[0037] In the developing device 300, the three-dimensional magnetic sensor

360 detects a magnetic flux density of a magnetic flux generated by the magnets

340 within the core 328, so as to reduce production cost, as the developing device 300 can determine a toner density without installing an added magnet.

[0038] The three-dimensional magnetic sensor 360 is disposed adjacent the developer roller 330. The three-dimensional magnetic sensor 360 is disposed externally to the container 301 and detects magnetic flux density components in the x, y and z directions of the magnetic flux generated by the magnets 340 through a wall of the container 301. The three-dimensional magnetic sensor 360 is fixed to an exterior surface of the container 301 by a fixing member 362 The fixing member 362 is fitted into a depression formed on the exterior surface of the container 301. In other examples, the three-dimensional magnetic sensor 360 may be adhered directly to the exterior surface of the container 301 with for example, a two-sided adhesive tape or an adhesive.

[0039] A processor 80 of the image forming apparatus 1 (cf. Fig. 1 ) calculates a composite value (e.g., size of a resultant vector) of the magnetic flux density components in the x, y and z directions of the magnetic flux detected by the three-dimensional magnetic sensor 360. Based on the composite value, the processor 80 determines a toner density of the developer within the container 301. As described above, determination of a toner density based on the composite value of the magnetic flux density components in the x, y and z directions can reduce an influence of an error in the position or angle for the attachment of the three-dimensional magnetic sensor 360. A memory 82 of the image forming apparatus 1 (cf. Fig. 1) may have stored thereon data indicating a correlation (for example, a correlation that will be described with reference to Fig. 15) between magnetic flux densities and toner densities measured by using the magnet 340 and the three-dimensional magnetic sensor 360 attached to the developing device 300.

[0040] The three-dimensional magnetic sensor 360 is disposed downstream of a layer regulation member 350 in a rotating direction of the developer roller 330.

This allows the three-dimensional magnetic sensor 360 to detect a magnetic flux density in a more stable manner where the amount of developer conveyed is constant, to improve the detection accuracy of the toner density. For example, the three-dimensional magnetic sensor 360 may be disposed immediately subsequent to the layer regulation member 350 in the rotating direction of the developer roller 330.

[0041] Fig. 15 shows an example of a correlation between magnetic flux densities and toner densities measured in an example image forming apparatus including the developing device 300. Since the developing device 300 has a constant distance between the magnets 340 and the three-dimensional magnetic sensor 360, the magnetic flux density increases in proportion to the toner density as illustrated. This correlation may be measured, for example, at a factory, and stored in the memory of the image forming apparatus in the form of the linear function, f = ax + b. However, the three-dimensional magnetic sensor 360 may be influenced by geomagnetism or an ambient temperature, the amount of developer within a toner bottle, etc. Consequently, the image forming apparatus can calibrate the correlation stored in the memory when the location for installing the image forming apparatus is changed or toner bottles are replaced. The processor 80 (cf. Fig. 1) carries out the calibration by acquiring outputs from the three-dimensional magnetic sensor 360 for example in a first state wherein the container 301 contains no developer, and in a second state wherein the container 301 contains developer with a predetermined toner density. It will be appreciated that the calibration may be carried out with other suitable methods.

[0042] During an operation of the image forming apparatus 1 , the processor 80 of the image forming apparatus uses an "average value” of the magnetic flux densities detected by the three-dimensional magnetic sensor 360 for example, during one rotation of the developer roller 330, to determine a toner density of the developer within the container 301, based on the correlation between magnetic flux densities and toner densities read from the memory. For example, the processor SOtakes samples of outputs from the three-dimensional magnetic sensor 380 during one rotation of the developer roller 330, and calculates a composite value of magnetic flux density from sampled magnetic flux density components in the x, y and z directions, so that an average value of composite values can be determined. Calculation of the average value reduces or eliminates influences of vibration caused by the rotation of the developer roller 330. For example, when the average value of detected magnetic flux densities is 14.9 mT, the processor can determine a toner density of about 8.5 weight% from the correlation shown as the linear function, for example, in Fig. 15. If the determined toner density is outside a predetermined operation range (e.g., a range for suitable operation, for example, of about 8% to 12%), the processor can command (or control) a toner feeding mechanism to adjust the toner density in the container 301.

[0043] In order to Improve the detection accuracy of a toner density, the processor 80 of the image forming apparatus 1 may determine a toner density of the developer within the container 301 based on an average value of sampled magnetic flux densities obtained by taking samples of magnetic flux densities detected by the three-dimensional magnetic sensor 360 during a plurality of rotations of the developer roller 330.

[0044] Further, in another example, the developing device 300 may include, instead of the three-dimensional magnetic sensor 380 disposed externally to the container 301, a three-dimensional magnetic sensor disposed adjacent the developer roller 330 while having a sensing surface within the container 301. Positioning the sensing surface of the three-dimensional magnetic sensor within the container 301 shortens a distance from the magnets 340 to the sensing surface of the three-dimensional magnetic sensor to increase an accuracy of the detection of the toner density.

[0045] Referring back to Fig. 1 , and with further reference to FIG. 16. the example image forming apparatus 1 includes a processor 80 to control the operation of various constituent elements of the image forming apparatus 1 , and a memory 82 to store various control instructions to be executed by the processor 80 and/or relevant data, as previously described. In some examples, with reference to FIG. 16, the memory (e.g., a storage device) 82 may include data and instructions 400 to carry out an operation 402 of receiving the composite value associated with the components in x, y and z directions of the three-dimensional magnetic flux density detected in the developer container 101 (cf. Fig. 2) that contains developer including toner and carrier, and to carry out an operation 404 of determining the toner density of the developer in the developer container 101 based on the composite value.

[0046] It is to be understood that not all aspects, advantages and features described herein may necessarily be achieved by, or included in, any one particular example. Indeed, having described and illustrated various examples herein, it should be apparent that other examples may be modified in arrangement and detail is omitted.