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MSD not only causes GRD, but also easily leads to the disconnection between the shaft, bunton and GR. The GRD characteristics are analyzed under the normal connection between them, the disconnection of the shaft from the bunton, and the disconnection of the bunton from the GR. The instability of the hoisting conveyance is mainly caused by the horizontal deformation of the GR. It can be seen from Fig.6 that the horizontal deformation of the guide rail in the same direction as the shaft deformation has a good follow-up to the shaft deformation, is highly correlated with the shaft deformation trend, and other horizontal directions are relatively low, so the main focus is on the deformation characteristic and law of the GR corresponding to the shaft deformation in the horizontal direction. Owing to the action mechanism of vertical compression deformation of shaft is different from other deformation types, it mainly focuses on inclination, bending, dislocation and horizontal section deformation of the shaft.

Starting from the position of 250m, the shaft is inclined in the positive direction of the x-axis, and the inclination rates are 0.2, 0.4, 0.6, 0.8 and 1mm/m, respectively. The GRD corresponding to the x-direction is shown in Fig.9. It can be found that the GRD is roughly linear and basically consistent with the shaft deformation. Its maximum deformation values are 49.1, 97.9, 146.5, 195.5 and 244.2mm, and it is reduced to a certain extent compared with the shaft inclination deformation. The GR within a certain depth from the upper surface of the shaft has both linear and fluctuating deformation. The period of the fluctuation deformation is 4m, which is the interval between adjacent buntons, and its amplitude and deformation range increase with the aggravation of the inclination deformation. The GR below the starting position of the inclination deformation only produces fluctuation deformation with a period of 4m, and the amplitude increases with the aggravation of the inclination deformation.

GRD in x-direction under inclination.

The lower GR has a stretching action on the upper part, but the support action of the bunton on the GR hinders the stretching, which leads to the reverse deformation of the GR with the bunton as the center, forming the fluctuation deformation in the upper part. The GR above the starting position of the inclined deformation makes the lower part tend to incline, and the constraint of the bunton on the GR restricts this deformation, resulting in the fluctuation deformation of the lower part. With the aggravation of the inclination deformation, the GRD basically increases linearly, and the amplitude and range of the fluctuation deformation increase, which has a good characterization relationship for the type and degree of the inclination deformation of the shaft.

To make the disconnection representative between bunton, GR and shaft under inclined deformation, the disconnection positions are selected at the upper, middle and lower parts of the shaft, which are 239, 119, 71 and 11m respectively. Figure10 shows the x-direction deformation of the GR under inclined deformation when the bunton is disconnected from the GR. In Fig.10a, the deformation is basically the same as the normal connection except near the disconnection position. At the disconnected position 239m, it is stepped with heights of 0.4, 1.8, 2.3, 4.3 and 4.9mm, respectively. It increases with the aggravation of the inclination deformation, and the change rate first increases and then decreases. The disconnected position is affected by the inclined deformation of the shaft, and the accumulated length of the GR below it is relatively small, resulting in a relatively small cumulative deformation energy of the GR near the lower part of the disconnection position, but the deformation energy near the upper part of the disconnection position is much larger than that of the lower part. When the bunton is disconnected from the GR, the deformation energy is released, so that the deformation of the GR in the upper part of the disconnection position is larger than that in the lower part, forming a stepped shape.

GRD in x-direction under inclination when bunton is disconnected from GR.

The deformation law near the disconnected position at 119 and 71m is basically the same, as shown in Fig.10b,c, with a sawtooth shape, the height increases with the aggravation of inclined deformation, and its minimum value is 3.1mm and the maximum value is 9.4mm. Since the disconnection position is located in the middle of the inclination deformation of the shaft, the difference in the accumulated deformation energy near the upper and lower part of the disconnection position is relatively small, and the deformation caused by the release of the deformation energy is basically the same, so it has a sawtooth shape. When the bunton and GR are disconnected at 11m as shown in Fig.10d, the GR on both sides of the disconnected position is deformed in reverse, showing a two-way sawtooth. The peak-to-peak value of the two-way sawtooth increases with the aggravation of the inclined deformation, and the minimum value is 9.8mm and the maximum value is 36.5mm, which far exceeds the allowable value of the GRD stipulated by the coal mine safety regulations. The stretching of the upper GR to the lower causes the upper bunton to be greatly stretched downward, induces the bunton to bend downward. When the upper bunton is disconnected from the GR, the bending deformation of the bunton at the disconnected position is greatly released, and the deformation at other positions is reduced to a certain extent, but the curvature is still large. Under the action of bending deformation, GR deforms to the side with smaller curvature, that is, the negative x-axis direction, forming a two-way sawtooth. Through the above analysis, it is found that the deformation laws of GR corresponding to different disconnected position are distinct. The bottom is stepped, the middle is sawtooth, and the upper part is two-way sawtooth. As the inclination deformation increases, its deformation amplitude augments. The disconnection position near ground has the greater impact on the GRD and is easy to cause hoisting accidents.

When the bunton is disconnected from the shaft at different positions, the x-direction deformation of the GR under inclination deformation is shown in Fig.11. The GRD law is basically unchanged at the disconnected position of 239, 119 and 71m, and the overall GRD law is fundamentally the same as that in the normal connection state. The period becomes 8m at 11m, as shown in Fig.11d, and it is twice the distance between adjacent buntons, but the amplitude basically unchanged. The disconnection between the shaft and the bunton loses its supporting effect on the bunton, the constraining effect of the disconnected bunton on the GR is invalid, and the GR deforms under the action of the interval bunton, which finally causes the period of the GRD to change at this position. Since the supporting effect of the upper bunton on the GR is much stronger than that of the middle and lower parts, the upper disconnection position easily affects the guide deformation. The disconnection of the bunton and shaft has less influence on the GRD than the separation of the bunton and GR, hence the attention should be paid to the connection state of the bunton and GR under the inclined deformation of the shaft.

GRD in x-direction under inclination when bunton is disconnected from Shaft.

The 140 to 120m segment of the shaft acts on the given of x-direction bending deformation, which is cosine type, the amplitudes are 1, 2, 3, 4 and 5mm in turn. The GRD in the x-direction is shown in Fig.12, there is approximately symmetrical bending from 146 to 119m, and the deformation ranges are (143.1, 119.1), (147.1, 119.1), (147.9, 119.1), (148.7, 119.1) and (149.8, 119.1) m, which are larger than the bending deformation range of the shaft. The maximum value of GRD is 0.99, 1.96, 2.93, 3.90, and 4.87mm, the corresponding position is 130.2m, and it is maximum deflection position of the shaft. There are differences in the GRD law on both sides of the maximum deflection, the right side is a smooth curve, and the left side is an inclined stepped curve. The inclined stepped curve is mainly due to the asymmetry of the bunton with respect to the maximum deflection position of the shaft. The bunton closest to the maximum deflection position of the shaft is located on its lower side, the maximum deflection of GR appears near the bunton under its action, and the distance relationship causes the above action on the lower side of the maximum deflection of the shaft to be much greater than the upper side, so the attenuation rate of the guide deformation is relatively slowly above the maximum deflection position of the shaft. Nevertheless, the effect of the farther upper adjacent bunton on it further increases its attenuation rate and it becomes the stepped shape. There is a corresponding relationship between the GRD and the bending deformation of the shaft. As the amplitude of the bending deformation of the shaft increases, the amplitude and range of the bending deformation of the GR enlarge, and the deformation law is the same. It indicates the sensitivity and reliability of the GRD to characterize the bending deformation of shaft.

GRD in x-direction under bending.

GRD appears periodic weak fluctuation outside a certain distance from the shaft bending region, its period is 4m, and its amplitude basically does not change with shaft bending deformation, which indicates that its influence on the GR is limited. From 119 to 106m, the deformation generally exhibits an inverted arch, and its amplitude is larger than other positions of the fluctuation deformation and it increases with the aggravation of the shaft bending deformation. The buntons constraint on the bending deformation of the GR makes it subject to a force in the negative x-direction, and drives the GR to move along the negative x-direction within a certain range, and finally the inverted arch occurs. The fluctuation is mainly caused by the constraint effect of bunton on the GR. The action of gravity leads the GR to deform in the vertical direction, and the constraints limit this deformation, which makes the upper half of the GR between adjacent buntons deforms along the negative x-direction, the lower half deforms along the positive x-direction, and the joint has the smallest deformation and is the starting point of periodic fluctuation. The maximum amplitude of the above fluctuations is only 0.02mm, the verticality and straightness meet the requirements of the GR installation specification, and it is generally straight, which further indicates the rationality of the initial connection parameters of the bunton, GR and shaft.

The disconnection positions are 11, 47, 83, 107, 119, 131, 143, 155, 179, 215 and 251m in sequence, and are all over the bending position and both sides of the shaft. Owing to the same of GRD law under different degrees of shaft bending deformation, it is studied that the shaft bending deformation amplitude of 1mm on disconnection. Figure13 shows the GRD law when the bunton is disconnected from the GR under bending action. The GR at the disconnected position deforms in opposite direction, and its amplitude is 0.38mm outside the range of shaft bending deformation, which is about 7 times the amplitude of the fluctuation deformation. The maximum amplitude occurs at 119m, and it is about 14 times the amplitude. This disconnection position is located at the junction of the shaft bending deformation, and the bunton below it is situated in the action area of the shaft bending deformation, so the GR below it is subjected to the above action, resulting in its abnormally prominent amplitude. The disconnected position at 131m is located in the middle of the bending deformation area of the shaft, the GR above it produces the reverse deformation and its amplitude is 5 times that of the fluctuation deformation, and the deformation below it is basically the same as that of the normal connection. Due to the bending deformation of the shaft, the end of the adjacent bunton at the disconnected position is bend towards the inside of the shaft, it causes the bunton near the disconnection position is bent downward, the lower GR is bent in the positive x-direction, and the upper GR is deformed in the opposite direction, which eventually leads to the GR occurs opposite deformation at the disconnected position between the bunton and GR.

GRD in x-direction under bending when bunton is disconnected from GR.

When the bunton is disconnected from the shaft under the action of the shaft bending deformation, the GRD is shown in Fig.14. When the disconnection is outside the shaft bending deformation, the period of the fluctuation deformation changes at the disconnection position and becomes 8m, and the amplitude basically does not change. When the disconnected position is located at 119m at the upper junction of the shaft bending deformation, the GRD law on the lower side of the disconnected position is basically the same as the normal connection. The deformation on the upper side of the disconnected position extends in the negative x-direction, which is mainly due to the bending effect of the lower GR in the positive x-direction and the reverse restraint effect of the upper GR in the disconnected position. When the disconnected position is located at 143m at the lower junction, the deformation decreases on the upper side near the disconnected position, and it increases on the lower side. The GR above this disconnected position is located in the bending deformation area of the shaft, it acts on the GR with an active force in the positive x-direction, thereby producing a pulling effect on the lower GR in the positive x-direction. The bunton at this disconnection position is located outside the bending deformation area of the shaft. When it is normal connection, it produces a negative x-direction constraint on the GR to slow down its attenuation rate of the bending deformation, the above restraint is eliminated under the disconnection state cause an increase in the attenuation rate of the GR bending deformation, which induces a diminution in the upper GRD near the disconnected position. and the bending deformation range of the GR and the deformation value below it increases.

GRD in x-direction under bending when bunton is disconnected from shaft.

When the disconnected position is 131m in the bending deformation area of the shaft, the deformation law near the disconnected position is basically the same as the normal connection, and the period and amplitude do not change significantly. When the disconnected bunton is located in the bending deformation area of the shaft, and the adjacent bunton has a strong bending deformation force on the GR at the same time, so even if a single bunton is disconnected from the GR, its force condition is basically unchanged, resulting in basically no change in its deformation law and amplitude. When the disconnected bunton is outside the bending deformation range of the shaft, the GR deformation period at the disconnected position changes, but the amplitude does not change. When the disconnected bunton is located at the junction of the shaft bending deformation, the deformation and period at the disconnected position change at the same time. The disconnection between the bunton and shaft under the bending deformation action has little influence on the deformation law of the GR, and the connection between the bunton and the GR should be focused on.

For a given shaft dislocation deformation in the x-direction from 130 to 90m, the amplitude is 1, 2, 3, 4 and 5mm at dislocation position of 130m and becomes 0mm at the 90m, and the attenuation rate is 0.025, 0.05, 0.075, 0.010 and 0.0125mm/m. The GRD under dislocation action is shown in Fig.15. The maximum deformation of the GR is 0.94, 1.88, 2.82, 3.78 and 4.72mm, and its position is 126.2m, which is higher than the dislocation position of the shaft, but its amplitude is basically unchanged compared with the dislocation amplitude of the shaft. The distance between the adjacent bunton makes it difficult to coincide with the position of the dislocation deformation of the shaft, and the dislocation deformation effect is transmitted to the GR through the bunton, so this effect causes the maximum deformation of the GR to occur near the bunton, and its position is moved up than the dislocation position of the shaft. The influence range of the dislocation deformation on the GRD is (143.5, 88.3), (143.9, 88.3), (146.7, 88.3), (146.9, 88.3) and (146.9, 88.3) m, which is much larger than the action scope of the shaft dislocation deformation. The shaft above the dislocation interface produces a stretching effect on the lower part, its lower part moves to the positive x-direction and expands the shaft deformation range, but the resistance from the SRSM to shaft restricts the transmission range of the above effect, which induces the deformation range of the GR is much larger than the action range of the shaft dislocation deformation. There are differences in the deformation law of the GR on both sides of the maximum amplitude, the upper side shows the attenuation trend of inclination deformation, and its attenuation rate is basically the same as the shaft dislocation deformation, accompanied by fluctuation deformation. The lower side has a bending deformation trend, and the attenuation rate first increases and then decreases as it moves away the maximum amplitude, which is mainly caused by the follow-up deformation of the shaft below the dislocation interface. The GRD corresponding to the shaft dislocation is a combination of inclination and bending. With the increase of the dislocation deformation, the slope of the inclined deformation of GR, the curvature of the bending deformation and the maximum amplitude increase, which are obviously different from the deformation feature of GR under shaft bending or inclination, and there is a good mapping relationship for the shaft dislocation.

GRD in x-direction under dislocation.

Figure16a shows the x-direction deformation of the GR when it is disconnected from the bunton under the action of the shaft dislocation, its position is 11, 47, 83, 107, 119, 131, 143, 155, 179, 215 and 251m, and the GR in the disconnected position generates the opposite deformation. The peak-to-peak value of the opposite deformation outside the shaft dislocation range is about 0.4mm, and it is about 20 times fluctuation deformation, which is mainly caused by the release of the interaction between the GR and bunton under the action of gravity. When the disconnection between the bunton and GR is 107 and 119m in the shaft dislocation area, the peak-to-peak value of the opposing deformation is 0.53 and 0.57mm, respectively, and its value increases less compared to outside of the shaft dislocation deformation region. Moreover, the peak-to-peak value at the junction of the shaft bending deformation is basically the same as that outside the shaft dislocation area. When the bunton is disconnected from the shaft at different positions, the GRD is shown in Fig.16b. The deformation decreases near the upper side of the disconnected position of 143m, the lower side augments, and its deformation mechanism is the same as at this position under the action of the bending deformation of the shaft, hence the explanation is not repeated here. Other disconnected position is basically unchanged in amplitude, and only the period becomes twice the fluctuation deformation. The deformation law is basically the same as the normal connection except the above disconnection position, hence the influence of shaft dislocation deformation on the GR has no obvious attenuation due to the disconnection between the bunton and GR.

GRD in x-direction under dislocation when connection is abnormal.

The shaft of the 130 to 110m segment imposes a given displacement in the x-direction so that its cross-section is approximately elliptical, the short axis is the x-axis and the long axis is the y-axis, and the amplitude occurs at the intersection of the outer wall of the shaft and x-axis. It attenuates uniformly on both sides along the y-axis and becomes 0mm at the intersection of the shaft and y-axis, and the attenuation curve is cosine. Figure17 shows the GRD when the amplitudes of the horizontal section change of the shaft are 1, 2, 3, 4 and 5mm in turn. The GRD from 134.9 to 107.4m is mainly affected by the horizontal section change, and the interval is basically unchanged with the aggravation of the horizontal section change. The deformation is generally trapezoidal, the middle section is a horizontal straight line accompanied by fluctuation deformation, and the transition area decays rapidly, generally an inclined straight line. With the increase of the deformation amplitude of the horizontal section change, the GRD from 134.9 to 130.5m shows the local arching phenomenon, which becomes more severe with the aggravation of the above deformation. The above phenomenon occurs near the junction of the action and influence zone of the horizontal section change. The bunton in action area follows the shaft to deform in the positive x-direction, and the GRD in the affected aera is less affected by the horizontal section change of shaft and bunton in affected area has a strong constraining effect on the guide deformation in the positive x-direction, and the GR in action area exists a strong stretching effect on GR in this position, which induces the local arching phenomenon.

GRD in x-direction under horizontal section change.

The amplitudes of the GRD are 0.33, 0.70, 1.04, 1.38, and 1.73mm corresponding to each horizontal section change, and it is a large attenuation relative to the shaft deformation. The fluctuation deformation amplitude from 107.4 to 73.1m augments with the aggravation of the horizontal section change, its amplitude is no obvious change rule from 73.1 to 46.9m, and the amplitude of 46.9 to 0m decreases. The above phenomenon is mainly caused by the strong constraint effect of bunton of the transition zone on the GR, and the strong stretching effect of the lower GR on the upper part. The deformation law of the GR is basically the same under the different amplitude of horizontal section change of the shaft, but there are obvious differences in the amplitude, which exists a good corresponding relationship between the horizontal section change of the shaft and the deformation law of the GR.

When the bunton is disconnected from GR, its position is 11, 47, 83, 107, 119, 131, 143, 179, 215 and 251m, respectively, and the GRD is shown in Fig.18a under horizontal section change. It generates the opposite deformation at the disconnected position, and its maximum peak to peak occurs in the transition zone of the horizontal section change at 107m and its value is 0.94mm. The disconnected bunton in the transition area locates in the outside of the shaft deformation and has little deformation effect on the GR, and the bunton below the transition area locates in the shaft deformation area and follows the shaft deformation to drive the GRD, which causes a large difference in force between adjacent buntons, and the maximum peak-to-peak value appears. In the horizontal section change area of the shaft at 119m, the peak-to-peak value is 0.43mm, and its value is basically the same as the disconnection position outside action area of the horizontal section change of the shaft. The disconnection between the bunton and GR in the transition area has the greatest influence on the GRD, which can easily lead to the abnormal deformation.

GRD in x-direction under horizontal section change when connection is abnormal.

Figure18b is the GRD corresponding the disconnection between the bunton and shaft under the horizontal section change of the shaft. The disconnection outside the action and transition area of the shaft deformation only changes the fluctuation deformation period near the disconnection position and its value is 8m, and the amplitude is basically unchanged. In the shaft deformation action area, the maximum peak-to-peak value is 1.12mm at disconnection position of 119m, and the peak-to-peak value at 107 and 131m in the upper and lower transition areas are 0.57 and 0.62mm respectively. The buntons on both sides of the disconnected position are located in the shaft deformation action area, are subjected to the pulling effect of the shaft in the positive x-direction, but the bunton at the disconnection position lacks the above effect, which eventually leads to local inverted arch near the position. The deformation principle of the GR at the disconnection position of the transition zone is the same as the above, except that one side of the bunton is located in the action zone, and the other side is located in the transition zone. However, the effect in transition zone is relatively weak, resulting in a relative lower peak-to-peak value. When the bunton is disconnected from the GR or shaft, the horizontal section change has a great influence on the GRD, so attention should be paid to the connection state.

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