JP4747140B2 - Method for obtaining pressure waveform for top shape of high-speed railway vehicle - Google Patents

Description

The present invention obtains a waveform of a pressure wave generated in a tunnel when a high-speed railway vehicle such as a Shinkansen (registered trademark) traveling at a high speed enters the tunnel, thereby relaxing a tunnel micro-pressure wave caused by the pressure wave. In particular, the present invention relates to a method for obtaining a pressure waveform with a head shape specified in three dimensions with high accuracy in a short time.

  One of the problems with high-speed rail cars is the tunnel micro-pressure wave that is generated when entering a tunnel. This tunnel micro-pressure wave is a sound wave that is mainly observed in the vicinity of the exit of the tunnel when a high-speed railway vehicle enters the tunnel. The component is an audible frequency (20 Hz or higher) and an ultra-low frequency (5 Hz to 20 Hz). ) Component. Since the pressure amplitude of the tunnel micro-pressure wave is proportional to the cube of the train speed, it is an important issue in the present day when high-speed traveling is progressing. The solution to this problem is how to determine the shape of the head of the vehicle.

The amplitude of the tunnel micro-pressure wave is proportional to the time rate of change of the pressure wave (sound traveling along the tunnel) reaching the tunnel exit (when observed stationary on the wall of the tunnel). Therefore, in order to reduce the tunnel micro-pressure wave, it is necessary to reduce the rate of time change (pressure gradient) of the pressure wave generated when entering the tunnel. As a basic measure, it is conceivable to reduce the cross-sectional area of the vehicle body or lengthen the head part of the vehicle body, but none of these are appropriate solutions because they impair the comfort of the cabin. Therefore, the present applicant has proposed the shape of the leading portion of Patent Documents 1 and 2 below.

In Patent Document 1, in obtaining the optimum cross-sectional area distribution of the head shape, analysis is performed using an axisymmetric model. In other words, a cylindrical body having a cross-sectional area distribution matched with the head shape of the vehicle was entered into the cylindrical shape so as to coincide with the cross-sectional area of the tunnel shape, and the pressure gradient generated thereby was examined.
In Patent Document 2, per the determination of the head portion shape, and based on the predetermined head portion shape, a pressure gradient distribution was studied by adding three-dimensional deformation aims to be a trapezoidal shape of the ideal . In other words, the three-dimensional characteristics of the shape of the top portion of the high-speed railway vehicle were considered to be preferable for reducing the pressure gradient by examining the confirmation work with various three-dimensional changes.
JP 2002-308092 A JP 2007-050746 A

  However, when designing the shape of the top part of a high-speed railway vehicle, the shape of the axisymmetric body, which is an approximation method, that is, the method of finding an optimal cross-sectional area distribution and designing an arbitrary three-dimensional shape from it, However, the improvement effect in the case of a three-dimensional body cannot be obtained as much as the improvement effect in the axially symmetric body. This is because the characteristic of the actual three-dimensional shape is not grasped due to an error derived from the approximation of axial symmetry. Ingenuity of the shape by the axisymmetric approximation is insufficient in accuracy, and there is a limit to the effect of reducing the gradient of the pressure wave that causes the tunnel micro-pressure wave.

  On the other hand, in order to improve the accuracy, the pressure waveform can be obtained with high accuracy by simulating the air flow when the train enters the tunnel with respect to the three-dimensional shape of the head shape, but the calculation amount is large. The problem is that it takes more than 10 hours per pattern. In order to perform the optimization, in the case of 3D, since the degree of freedom of design (for example, several thousand patterns) is large and the phenomenon itself is complicated, the calculation amount (work amount) becomes enormous, It took a long time and was costly. Further, the device of the three-dimensional shape has a problem that it is difficult to quantify the shape characteristic and its influence because there is no easy-to-understand index such as the cross-sectional area (cross-sectional area change rate).

  Accordingly, an object of the present invention is to provide a method for obtaining a pressure waveform generated at the time of entering a tunnel, in which a pressure gradient with respect to the shape of the head portion can be estimated in a short time in order to solve such a problem.

The method for obtaining the pressure waveform for the top shape of the high-speed rail vehicle according to the present invention is to specify the shape in three dimensions for the top portion from the tip of the high-speed rail vehicle to the travel direction position where the cross section orthogonal to the travel direction is maximum. This is a method for obtaining a pressure waveform generated when the arbitrarily created high-speed railway vehicle having the top shape enters the tunnel, and is arbitrarily selected on the yz projection plane orthogonal to the x axis in the vehicle traveling direction. The impulse response of the pressure wave caused by the change in the cross-sectional area of the unit amount is obtained at a plurality of positions representing the subdivided region, the impulse response is stored as a database, and the head portion is created for the arbitrarily created head portion shape. The area cross-sectional area change rate for each subdivided area of the shape and the corresponding impulse response of the database are convolved and integrated to be summed. .

In addition, the method for obtaining a pressure waveform for the shape of the leading portion of the high-speed railway vehicle according to the present invention is a three-dimensional shape for the leading portion from the tip of the high-speed rail vehicle to the traveling direction position where the cross section orthogonal to the traveling direction is maximum. This is a method for obtaining a pressure waveform generated when a head-shaped high-speed rail car that is arbitrarily created and enters the tunnel, and is on a yz projection plane orthogonal to the x-axis in the vehicle traveling direction. An impulse response of a pressure wave caused by a change in cross-sectional area of a unit amount is obtained at an arbitrary plurality of positions , the impulse response is stored as a database, and an impulse response representing coordinates (y, z) is represented by r (X , Y, z) as a function, the x coordinate of the outer surface of the head shape in coordinates (y, z) as a function as u (y, z), and the vehicle on the yz plane In the region σ where the vehicle exists when
The pressure waveform q (X) of the arbitrarily created head shape is obtained by performing the integral calculation.

In addition, the method for obtaining a pressure waveform for the shape of the leading portion of the high-speed railway vehicle according to the present invention is a three-dimensional shape for the leading portion from the tip of the high-speed rail vehicle to the traveling direction position where the cross section orthogonal to the traveling direction is maximum. This is a method for obtaining a pressure waveform generated when a head-shaped high-speed rail car that is arbitrarily created and enters the tunnel, and is on a yz projection plane orthogonal to the x-axis in the vehicle traveling direction. An impulse response of a pressure wave caused by a change in cross-sectional area of a unit amount is obtained at an arbitrary plurality of positions , the impulse response is stored as a database, and an impulse response representing coordinates (y, z) is represented by r (X , Y, z), expressed as a function, and the x coordinate of the outer surface of the head shape at coordinates (y, z) is expressed as a function as u (y, z). The area σ where the vehicle is present when the vehicle is projected onto the yz plane, where A (x) is the area surrounded by the vehicle body outline cut from the top shape and S is the cross-sectional area of the tunnel In
The pressure waveform q (X) of the arbitrarily created head shape is obtained by performing the integral calculation.

Further, in the method for obtaining the pressure waveform for the top shape of the high-speed rail vehicle according to the present invention, impulse responses at positions on the yz projection plane other than the impulse response stored in the database are stored in the database. It is preferable to obtain the pressure waveform for the top shape of the high-speed railway vehicle, which is obtained by interpolation from the impulse response.

  The head shape optimization method according to the present invention is a method for optimizing the head shape of a high-speed railway vehicle for which a pressure waveform is obtained by any of the methods described above. A procedure for changing the pressure waveform by moving the origin position of the derived impulse response along the X axis is performed a plurality of times, and a pressure waveform showing a superior value is obtained from the pressure waveforms obtained by the plurality of procedures. And selecting a new head portion shape by displacing the shape of the vehicle surface by an amount corresponding to the amount of movement of the impulse response waveform in the selected pressure waveform.

In the optimization method of the head shape according to the present invention, the movement of the impulse response along the X axis is performed by squaring the difference between the preferable pressure waveform and the pressure waveform, and on an arbitrarily set waveform. It is preferable to make the residue integrated in the evaluation interval a residual and bring the residual close to zero.
Further, the head shape optimization method according to the present invention differentiates the impulse response with respect to the X-coordinate when the impulse response moves along the X-axis, and determines the optimum moving direction and amount of movement based on the differential value. It is preferable to obtain it.

  Moreover, it is preferable that the head part shape according to the present invention is obtained by any one of the head part shape optimization methods.

Therefore, according to the present invention, by using the impulse response created in the database, a pressure waveform is obtained in a short time for the top part shape of the high-speed railway vehicle created in three dimensions, and the pressure gradient is confirmed, that is, The effect on tunnel micro-pressure wave can be confirmed.
Further, according to the present invention, an optimized head shape can be created in a short time by the process of moving the impulse response on the X axis.

  Next, a method for obtaining a pressure waveform according to the present invention will be described below with reference to the drawings. First, FIG. 22 shows the pressure gradient distribution of the compression wave when traveling at a speed of 270 km / h, which is caused by different head shapes (patterns 1 to 4). It shows the pressure gradient distribution of the compression wave generated at the time of entry into the tunnel at the head of the vehicle. Specifically, the pressure change of the compression wave observed at a predetermined location in the tunnel is differentiated with respect to time. The vertical axis represents the pressure gradient, and the horizontal axis represents time. In the example shown in FIG. 22, the train speed is 270 km / h, and in the other examples shown below, the train speed is 300 km / h. The difference in the train speed is the difference between the magnitude of the pressure waveform and the gradient. However, there is no essential difference in what is described below.

  In FIG. 22, v is the vehicle speed, and L is the length of the leading portion of the vehicle. The origin 0 of the time at the observation point is the time when the sound wave generated at the moment when the vehicle tip passes through the reference plane fixed at a tunnel entrance so as to be orthogonal to the rail direction reaches the observation point. Therefore, if the observation point is at a position where the distance B has entered from the tunnel entrance, the time is deviated from the entry of the vehicle by B / s if the speed of sound is s.

  Since the micro-pressure wave generated when the railway vehicle enters the tunnel is proportional to the pressure gradient expressed in this way, it is effective to reduce the maximum value of the pressure gradient in order to reduce the micro-pressure wave. Therefore, in designing the head portion shape, the pressure gradient with the maximum value reduced is reduced by reducing the difference between the values of the maximum portions P11 and P12 and the value of the valley portion T10 as in the pattern 4 shown in FIG. The goal is to have a waveform (hereinafter referred to as “pressure waveform”).

  If the maximum cross-sectional area of the vehicle (the area surrounded by the outline cut by the plane perpendicular to the traveling direction) is the same, the pressure change (pressure) that occurs when the same tunnel is run at the same speed This is because the gradient is integrated, and the area between the pressure waveform curve and the horizontal axis is constant. Therefore, when determining the shape of the head of the railway vehicle, the pressure waveform as shown in FIG. 22 is obtained for the three-dimensionally created head shape of the pattern, and the characteristics against the tunnel micro-pressure wave are confirmed. . At this time, it is necessary to calculate a pressure waveform for each designed head portion shape. In this embodiment, a method for easily obtaining a pressure waveform for an arbitrary head portion shape is provided.

  Here, FIG. 1 is a side view showing the shape of the leading portion of the high-speed railway vehicle. When considering the three-dimensional shape of the vehicle head, the vehicle longitudinal direction along the rail is x (the point closest to the vehicle tip is the origin and the rear is positive), and the vehicle width along the sleeper orthogonal to x The direction is y, and the vehicle height direction perpendicular to the ground perpendicular to the xy plane is z.

  In the present embodiment, first, the tunnel entrance shape projected on the yz plane orthogonal to the x axis in the vehicle traveling direction is considered regardless of the specific head shape, and at any position on the projection plane, the unit Examine the impulse response of the pressure wave caused by the change in the cross-sectional area of the quantity. The impulse response is obtained by the following virtual experiment. FIG. 2 is a diagram illustrating the tunnel entry of the driving body in obtaining the impulse response. FIG. 3 is a diagram showing sample points of the impulse response in the yz plane. The impulse response refers to a pressure wave gradient generated by each driving body 10 when a cylindrical object (driving body) 10 having a rounded tip is driven into the tunnel 100.

The sample points of the impulse response are set in the yz plane by the number of positions that are accurately required for obtaining the pressure wave due to the head shape. In this embodiment, there are 25 locations as shown in FIGS. The 25 sample points are arranged corresponding to the position where the railway vehicle passes through the tunnel 100, and are arranged in a lattice shape in accordance with the outline 20 of the general section as shown in the figure. In this yz plane, the height of the rail surface is set to z = 0, the center position in the width direction of the vehicle is set to y = 0, and the height direction coordinate value Z and the width direction coordinate value Y are set as shown in the figure. Each sample point is set at a position.

The driving body 10 is formed so as to be axisymmetric so as not to generate force in the vertical and horizontal directions. Specifically, as shown in FIG. 4, it is a semi-infinite cylindrical shape whose tip is formed of a paraboloid of revolution, and is formed to be sufficiently thin compared to the cross-sectional area of the tunnel 100, with a diameter at the maximum diameter portion. 200 mm. A section having a maximum cross-sectional area at a position of 100 mm from the tip and a section from the tip to 100 mm is a paraboloid of revolution with a constant cross-sectional area change rate. And the back is formed so that it may narrow down so that it may go to back in order to cancel the volume which a boundary layer excludes air current. The method of squeezing is determined after trial and error by repeating simulation from the initial shape based on the theoretical solution, and has a diameter φn (mm) at the position of the distance Xn (mm) from the tip as shown in the figure (n = 1, 2, 3 ...).

  When this driving body 10 is driven into the sample position in the tunnel 100 at the same speed U = 83.333 m / s as the train speed, a pressure wave having a waveform as shown in FIG. 5, that is, an impulse response is generated. Here, five of the 25 sample points are shown, but in actuality, impulse responses generated by the 25 locations are obtained. The 25 sample points are numbered 1 to 25 in order from bottom to top and from left to right as shown in FIG. FIG. 5 representatively shows five impulse responses indicated by intermediate height numbers 3, 8, 13, 18, and 23 extracted from them.

  The impulse response by the driving body 10 is obtained using a conventional method such as CFD analysis. The impulse response is not affected by the proximity effect near the tunnel entrance and the local propagation near the driving object, and the position where the finite amplitude sound wave penetrates from the tunnel entrance to the extent that it does not deform during propagation due to the nonlinear effect. The pressure wave gradient observed at the measurement point provided on the tunnel wall is divided by the projected area of the driven object.

  The impulse response shown in FIG. 5 is based on the time when the pressure wavefront generated at the time when the tip of the driving body 10 passes through a reference plane fixed and fixed at the tunnel entrance so as to be orthogonal to the rail direction reaches the measurement point. The axis X indicating the position on the waveform is shown as the horizontal axis obtained by multiplying the elapsed time from that by the train speed U. The pressure waveform as the original data of observation is expressed on the time axis, but by converting in this way, it can be superimposed on the coordinate system x of the same scale as the train, and the X axis and the x coordinate are regarded as the same. To express. That is, the relationship between the X axis and the x coordinate is that the sound wave generated at the moment when the position of the coordinate x of the train passes the reference plane at the tunnel entrance is recorded at the X position on the horizontal axis on the waveform graph. Therefore, X has the same dimension as the length and represents the corresponding position of the pressure wave source.

  Further, the waveform of the impulse response at each sample point has the same integrated area. The original data of the pressure gradient waveform has a dimension of [pressure divided by time divided by area], and the dimension of [pressure divided by length divided by area] when the time axis is coordinate-converted on the X axis. In FIG. 5, the integrated area is normalized to be “1” and expressed as having a dimension of [1 ÷ length]. The impulse response is defined in an infinite domain with respect to X. Based on this assumption, an integration formula is presented, but the range of X indicating a significant amplitude in calculation is a finite interval including the origin. There is no problem in ignoring the hems at both ends. The response shown in FIG. 5 asymptotically approaches a function of a constant multiple of [{(X ^ 2) + S / π} ^ (-3/2)] in X → −∞. Also, asymptotically approaches 0 in X → ∞. Actually, it becomes about 1 / 1,000,000 of the maximum value near X = 11 m.

  It can be understood from the waveform of the impulse response shown in FIG. 5 that the impulse response differs depending on the entry position of the driving body 10 with respect to the tunnel 100 in the yz plane, that is, the position of the sample point. In particular, the sample point 3 close to the wall surface of the tunnel 100 has a large impulse response peak value, and conversely, the peak value decreases as the distance from the tunnel wall surface increases. Then, the closer to the side surface of the tunnel 100, the steeper the slope decreases after passing through the tip of the driving body 10.

  In addition, the impulse response is such that X before the driving object 10 passes through the tunnel entrance reference plane rises gently from the negative position in the tunnel, and is attenuated within a short elapsed distance after passing. I understand. Further, the impulse response at the sample point 3 near the side surface of the tunnel once becomes negative and rises again after the tip of the driving body 10 passes through the tunnel entrance reference plane. From this, the impulse response is the expansion wave component due to the free-end reflected wave at the opening on the entrance side and the wall surface (right side of FIG. 3) opposite to the tunnel wall surface (left side of FIG. 3) closest to the sample point on the tunnel entrance surface. It can be seen that it is affected by the reflected compression wave that has reflected and returned. The impulse response reproduces wave phenomena such as three-dimensional sound reflection and diffraction that occur in the vicinity of the tunnel entrance at the time of entering the tunnel in this way, which enhances the accuracy of this method.

  For such an impulse response at each sample position, when comparing the sharpness of the waveform with the peak height, in the vehicle body width direction (y direction), as described above, for example, the peak on the sample point 3 side close to the tunnel side surface is obtained. It is high. Although not shown in FIG. 5, in the vehicle body height direction (z direction), a result was obtained in which the peak was higher at a higher sample point. Therefore, it was found that the impulse response differs depending on the sample position, and there is nonuniformity depending on the position. And in this embodiment, the impulse response calculated | required about these some sample points is preserve | saved as a database, The pressure waveform of the said head part shape by tunnel entry is calculated | required by synthesize | combining these according to arbitrary head part shapes.

The pressure gradient waveform q (X) generated by the head shape is an impulse response r (X, y, z) representing coordinates (y, z) on the yz projection plane and a function u that specifies the head shape. Using (y, z), it can be obtained by the integral calculation of the following equation (1). The horizontal axis of the pressure gradient waveform q (X) is obtained by coordinate conversion on the X axis in the same manner as the impulse response. The integration range σ in the following equation is a region where the vehicle exists when the vehicle is projected onto the yz plane. Further, since the database has only the impulse response at the sample point as described above, the impulse responses at other locations are obtained by interpolation using the impulse response of the database.

  For the three-dimensional shape of the vehicle head, for example, as shown in FIG. 6, a contour map is created with contour lines viewed from the front. In this case, the vehicle surface position corresponding to the x coordinate of the vehicle head portion (the coordinate system with the front end as the origin and the rear is positive) is plotted on the yz plane. Thus, the x-coordinate value of the vehicle surface is specified on the yz projection plane by the function u (y, z) of y and z, and expresses the head portion shape.

  By the way, in this embodiment, Formula 1 is derived on the assumption that the influence of the vehicle cross-sectional area on the pressure waveform is linear, and that the entire pressure waveform is approximated by the synthesis of the pressure waveform generated by each part. ing. First, the derivation process will be described. FIGS. 7 and 8 are views showing the concept of the formula 1 using an impulse response for the three-dimensional pressure waveform of the present embodiment. In particular, FIG. 7 is a diagram showing the concept of the cross-sectional area response in the axisymmetric model, and FIG. 8 is a diagram showing the concept of the cross-sectional area response in the three-dimensional model using the impulse response. That is, when considering the impulse response of a region divided as necessary in the yz plane, if the division is made minute, the result is integration with respect to the response at an arbitrary cross-sectional position.

  Also here, the x coordinate is 0 at the front end of the vehicle and positive at the rear side. The input is the cross-sectional area change rate s (x) = dA / dx, and the output is q (X) obtained by differentiating p (X) expressed by converting the pressure into the corresponding position (coordinate X) of the pressure wave source. = Dp (X) / dX. The cross-sectional area change rate s (x) has a dimension obtained by dividing the area by the length, and q (X) has a dimension obtained by dividing the pressure by the length.

Further, the impulse response r (X) has “q per unit area”, that is, a dimension obtained by dividing the pressure by the volume, and depends on the train speed and the tunnel shape. The velocity and tunnel cross-sectional area can be normalized by a predetermined calculation formula, and it is estimated that it can be expressed by the reciprocal of the representative diameter of the tunnel.
r (X) to (proportional coefficient) · (ρU 2 / S) · Q [X / D]
ρ is the air density, S is the cross-sectional area of the tunnel, Q is a function indicating a waveform, and if the relative geometric shape of the train entry position with respect to the tunnel shape is unchanged, it is considered that it does not change even if the scale is changed. The function D is a dimension representative of the diameter of the tunnel, for example, the diameter of a circle having the same area as the tunnel cross-sectional area. Further, when the effects of U and S are normalized, the value obtained by integrating r (X) is a constant, and the waveform normalized so that the integrated value becomes “1” in the same manner as the waveform shown in FIG. As the representative diameter D of the graph increases, the peak of the graph is inversely proportional to the peak, and the apex becomes lower and the skirt expands.

In the concept of the axially symmetric model shown in FIG. 7, as expressed by the following equation (2), a single impulse response r (X) that does not depend on the head shape and the change in cross-sectional area corresponding to the head shape. A pressure waveform is obtained by convolution integration of the rate s (X).

On the other hand, the vehicle shape projected on the yz plane is divided into an arbitrary number N, and impulse responses r1 (X), r2 (X),... RN (X) representing the divided areas are respectively May show different waveforms. The pressure waveform having the same head shape as that obtained in FIG. 7 is obtained by adding a plurality of impulse responses as shown in FIG. That is, the sum of the area cross-sectional area change rates s1 (X), s2 (X),... SN (X) for each divided area of the top shape and the impulse response representing each area is a convolution integral. It is calculated by the formula.

When the division on the yz projection plane is made fine, the impulse response is a function r (X, η, ζ) for the coordinate value η in the sleeper direction and the coordinate value ζ in the height direction, and the pressure waveform is As shown in the following equation, the area integration of convolution is obtained.
However, the numerical values b and Zmax indicating the integration range are determined so that the integration range covers the range in which the vehicle exists on the yz projection plane.

The rail direction x-coordinate value of the head shape surface projected onto the coordinate point (η, ζ) on the yz projection plane of the head shape is represented by u (η, ζ) (traveling direction). , And the outward normal vector on the surface is in the positive direction of x, and u (η, ζ) is uniquely determined). At this time, the local cross-sectional area change rate becomes a delta function δ (X−u (η, ζ)) as shown in the following equation. Since the local cross-sectional area change rate is a constant 0 in the area where no train exists, the integration range is limited.

Therefore, the convolution part can be solved, and the pressure waveform becomes area integration as shown in the following equation, so that Equation 6 is derived. And the pressure waveform calculated | required by this Formula corresponded with the pressure waveform calculated | required by Formula 1.

  Therefore, in the present embodiment, the pressure waveform is obtained by using the arithmetic processing device and executing the arithmetic processing of Formula 1 for the top shape of the high-speed railway vehicle. In the arithmetic processing unit, a pressure waveform output program for executing the arithmetic processing of Formula 1 is stored in the storage unit. In order to execute the pressure waveform output program, as described above, an impulse response is obtained in advance according to the train speed for the ground shape of the tunnel, and is stored in a database. The arithmetic processing unit also stores a head shape optimization automatic program described later.

  The pressure waveform output program is executed as follows. With respect to the head shape shown in FIG. 1, surface mesh (triangle or quadrangle) data specifying the surface shape is given. Then, the waveform of the impulse response for all nodes is obtained by interpolation from the waveform of the impulse response stored in advance in the database. At this time, since the obtained waveform of the impulse response is an amount per unit area of the triangular or quadrilateral element on the yz projection plane, it is referred to as a unit response waveform r (X, y, z).

The unit response waveform of each node of the head shape is displaced corresponding to the vehicle shape so that the original waveform is translated on the X axis. That is, the tip of the driving body 10 is displaced so as to correspond to moving to the vehicle surface at the position on the projection plane, and is expressed as r (X−u (y, z), y, z).
The unit response waveform is a constant that does not depend on the position on the yz projection plane, and the ratio of the tunnel cross-sectional area to the maximum cross-sectional area of the vehicle at a constant train speed. When is fixed, it correctly reflects the property that the maximum wave height of the pressure wave (total pressure increase obtained by integrating the pressure gradient) becomes a constant.

In order to improve the accuracy of this approximation method for obtaining the pressure gradient waveform, it is effective to perform the following correction on the unit response. The air in front of the train in the tunnel is expelled as the train travels, and is ejected from the tunnel entrance. However, as the vehicle head enters, the flow path to be ejected is narrowed by the amount occupied by the vehicle. Therefore, it has the same effect as the tunnel becomes narrower, and the total pressure increase caused by the increment of the unit cross-sectional area is increased, so that the unit response is multiplied by a scalar and φr (X−u (y, z), y, z ). As a result, the integral value corresponding to Equation 7 is multiplied by φ. The function φ is expressed by using the area A (x) (the area projected in the x direction) surrounded by the vehicle body outline obtained by cutting the vehicle head at the coordinate x, and the tunnel cross-sectional area S (constant). What is represented by the formula is effective.

In the formula 1, the cross-sectional area of the flow path in the tunnel that changes due to the approach of the vehicle head is not considered. However, in reality, the flow path area corresponding to the cross-sectional area of the tunnel changes gradually from time to time depending on the shape of the top part, which increases in cross-sectional area toward the rear, so the position behind the front is the wave source. The unit response is stronger. Therefore, it is desirable to correct the equation (1) to obtain the pressure waveform in the following equation where the correction term of the equation (8) is applied.

  Another correction that is effective to improve accuracy is to reproduce the effect of sharpening the unit response by reducing the distance from the vehicle surface to the tunnel side. The total pressure rise does not change because the area of the flow path is unchanged, but if the cross-sectional shape of the flow path is an ideal circle and the unit cross-sectional area of the vehicle increases in the center, the effect of the cross-sectional area increase is It extends almost uniformly throughout the channel. However, in a flow path with a narrow cross-sectional shape, such as partly blocked by a vehicle, if the same amount of unit cross-sectional area increases in a narrow part surrounded by the vehicle, the tunnel wall and the floor surface, Since the pressure gradient concentrated on the surface is generated, the waveform is sharpened. Specifically, the degree to which the focused node is closed by the vehicle and separated from the wide part of the channel cross-section (the degree of occlusion) is quantified, and the horizontal axis and vertical axis of the unit response are related to the degree of occlusion. Scale the axes at the same time to ψr (ψ (Xu (y, z), y, z).

In this operation, the pressure gradient waveform has only a sharp peak, and the integral value of the integral equation corresponding to the integral equation (Equation 7) remains unchanged. The function ψ is the entire cross section around the point (y, z) in the flow path obtained by subtracting the cross section of the vehicle from the entire cross section of the tunnel on the cut surface at the position where the x coordinate is u (y, z). Using the ratio of the area G within the radius of a circle having the same cross-sectional area to the area F of the entire cross-section of the tunnel within the same circle, it is effective to express it using Equation (10).

In the equation 1 or the equation 9 obtained by correcting the equation 1, the unit cross-sectional area increment at a point on the left side corresponding to an arbitrary point on the right side of the top vehicle portion having a symmetrical shape is equal to the pressure gradient waveform. Is generated. However, since the vehicle actually travels on the left side of the double-track tunnel, the left side surface close to the tunnel wall surface is limited in terms of spatial expansion, resulting in an increase in the rate of pressure increase, resulting in a locally strong pressure gradient. That is, the unit response waveform is sharpened. Therefore, it is desirable to obtain the pressure waveform in the formula 11 obtained by correcting the formula 1 to the formula 10 or the formula 12 obtained by performing the same correction on the formula 9.

Therefore, by integrating the unit response waveform over the entire surface mesh surface, a pressure waveform of the entire head shape as shown in FIG. 22 is obtained. The area at the time of integration is a projected area on the yz plane. Integration is performed on the discretized mesh as follows:

In Equation 13, the integral is discretized as a sum total at all nodes and approximated. When the coordinate value of the node i is (xi, yi, zi), the unit response at the position (yi, zi) is the argument σi of the area σi of the representative portion of the node projected on the yz plane. A sign function sgn () that can take values of -1 (negative), 0 (0), 1 (positive) depending on the sign, and is the inner product of the outward normal vector of the element and the unit basis vector of the x axis The sum is obtained by determining and multiplying the code according to the sign of (2) and multiplying the two kinds of correction terms. i is a subscript. Thus, by the operation of multiplying by the sign function, the reservation about the uniqueness of the function u (y, z) representing the x coordinate value of the head shape surface is canceled at the time of actual calculation. For example, even if it is a shape where x value contours projected on a yz projection plane having a protruding driver's seat canopy overlap, it can be applied without restriction.

  Therefore, in the present embodiment, the impulse response is stored in a database in advance, and a pressure waveform is generated in a short time for the top shape of the arbitrarily created high-speed railcar by performing arithmetic processing based on the expression expressed in Equation 1. Can now get. FIG. 9 shows an example in which the pressure gradient waveform generated at the time of tunnel entry is obtained by this embodiment. FIG. 9 is a side view showing two types of three-dimensional top shapes as shapes 7 and 8. For each of these two types of shapes, the conventional method of directly simulating the unsteady phenomenon of tunnel entry with a CFD using FEM for a three-dimensional train, and the method of obtaining the waveform approximately by Equation 12 according to this embodiment The pressure gradient waveform was calculated by both the method for obtaining the pressure gradient waveform and displayed as waveforms 701, 702, 801, and 802.

Although this embodiment is an approximation method, this embodiment gives a pressure gradient waveform with high accuracy including the position and size of the pressure waveform and the characteristic swells slightly existing near the top of the waveform. I understand that. The error was 3% with respect to the maximum value.
In the conventional method, the calculation processing by the calculation processing device takes ten hours, but in the present embodiment, the pressure waveform can be output in a few minutes, and it is necessary for the calculation processing of a huge pattern for optimization. It has become possible to significantly reduce the work time.

  Next, in order to make it easy to understand the explanation using the mathematical formulas, the procedure of this method will be described for a simplified shape. Here, an example is shown in which the unit response is not corrected but is performed based on Equation (1).

FIG. 10 is a diagram showing a simplified train head shape and an operation for obtaining a pressure gradient waveform at the time of tunnel entry by this approximation method. The vehicle head portion outer shape 200 is indicated by a thick solid line, the vehicle general portion is indicated by an adjacent broken line, and it is not necessary to calculate the general portion.
The vehicle head outer shape is subdivided as many as required for accuracy. The number of divisions is usually several hundred to several thousand, but here, in order to facilitate the explanation, four divisions represented by representative points 201, 202, 203, and 204 are assumed, and the projected area on the yz section represented by each is For convenience, it shall be equal. The representative points 201, 202, 203, and 204 are displayed at the X coordinate position having the same value as the x coordinate in the rail direction.

A unit response is defined at the representative points 201, 202, 203, and 204. First, in FIG. 10, a common impulse response is given to all. Waveforms 211, 212, 213, and 214 are obtained by multiplying each unit response by a common projected area. Waveforms 211, 212, 213, and 214 are translated on the X axis by the x coordinate value of the representative point, that is, u (y, z), and the respective origins are indicated by alternate long and short dash lines. And the sum total of such waveforms 211, 212, 213, 214 is the pressure gradient waveform 220 for this head shape . Using a common impulse response is equivalent to performing an axisymmetric approximation. A waveform 220 in FIG. 10 represents the result of reducing the maximum value of the pressure wave gradient by devising the vehicle shape by axisymmetric approximation, that is, devising the cross-sectional area distribution A (x).

FIG. 11 is a calculation example in which an impulse response representative of the cross-sectional position is given to the representative points 201, 202, 203, and 204. Waveforms 231, 232, 233, and 234 are obtained by multiplying each unit response by a common projected area. The sum of the waveforms 231, 232, 233, and 234 is the pressure gradient waveform 240 in the shape of the head portion . As shown in FIG. 5, since the impulse response has spatial non-uniformity on the yz plane, the waveform 240 considering the three-dimensionality has a different shape from the waveform 220 of FIG. . Such a difference between the waveform 220 and the waveform 240 expresses that the optimization based on the axisymmetric approximation is insufficient in accuracy.

  By the way, since there is no easy-to-understand index for the three-dimensional shape in determining the head shape, it is necessary to create a large number of three-dimensional shapes with subtle changes and obtain a pressure waveform for each. It was. However, in that case, only the micro-pressure wave reduction is not an element for determining the head portion shape. This is because the front of the vehicle is the face of a railway vehicle, and its shape has a very important meaning in terms of design. Therefore, it is preferable that the vehicle head is excellent in design, so that the shape is determined based on the shape of the head by the designer, and a function to reduce micro-pressure waves is added to the shape. Is desired.

  As described above, the pressure waveform can be obtained for an arbitrary head shape using the impulse response database as described above. Here, FIG. 12 is a diagram showing a pressure waveform in each head part shape, and the pressure waveform in the head part shape shown in FIG. In this pressure wave, peaks P1, P2, and P3 are formed at three locations, and in particular, a valley portion T between the peaks P1 and P2 is greatly depressed. Therefore, in order to reduce the maximum value of the pressure gradient, it is desirable to reduce the values of the peaks P1 and P2, raise the valley T and average the top, and obtain a pressure waveform as shown in the pattern 14. Note that pref used on the vertical axis in FIG. 12 is a reference pressure value for normalization, 2053.5 Pa, and U is a train speed, 83.333 m / s.

Conventionally, when the shape of the basic head portion shown in FIG. 1 is designed and a pressure waveform is obtained for it, as described above, work for making the pressure wave more ideal has been performed. . However, since it is difficult to quantify the relationship between the shape feature and the effect that feature has on the waveform, trial and error must be repeated to obtain the leading shape of the desired pressure waveform. It took time. This is the solution of the partial differential equation where the pressure waveform is the flow, and the head shape forms the boundary condition, and the pressure waveform and the head shape are only implicitly related in the equation. Due to that. In other words , it was necessary to create and verify how many models the ideal pressure wave waveform can be obtained by deforming the shape of the entire head portion as a base.

In this embodiment, in order to solve such problems, an automatic program for optimizing the head shape using a database of impulse responses is proposed.
Based on the impulse response database constructed for the tunnel in advance, the pressure waveform generated by the head shape is obtained at the position of each surface point of the head shape, and the amount corresponding to the x coordinate of each surface point It is the essence of the operation of this method that the unit response waveform translated only in the X-axis direction is approximated by a method in which the unit response waveforms are weighted with the projected area and added together. The amount of movement in the X-axis direction reflects the shape. Therefore, changing the x coordinate of the surface point at the point (y, z) on the yz cross section and moving the origin position of the unit response forward or backward on the X axis are as follows: Respond directly. Using this fact, the origin position of the unit response for which the waveform is calculated is translated on the X axis to check how the pressure waveform changes. Then, the head shape is optimized by obtaining a new head shape from the movement result of the unit response in which the micro-pressure wave is reduced.

  Moving the origin position of the unit response on the X-axis is an image of moving the tip position of the virtual driving body 10 that is the source of the unit response waveform that is located on the surface of the top portion shape. The tip of the virtual driving body 10 is a point that exists in space, and in addition to the point corresponding to the unit response obtained by interpolation so that the set of points forms the head shape, it is necessary for accuracy. There are multiple numbers. Then, as an effect that the tip position of each virtual driving body 10 arranged in the space is displaced in the x direction, a change is given to the shape of the head portion, and the movement is performed along the X axis representing the waveform in association with the change. Corrections are also made to the pressure waveform.

  Accordingly, in order to obtain an ideal pressure waveform, the origin position of each unit response is moved along the X axis to calculate the pressure waveform a plurality of times, and the pressure gradient is determined from the plurality of pressure waveforms. Select the one with the smallest maximum value as having an excellent pressure waveform. Then, the shape is displaced by an amount corresponding to the movement amount of the selected impulse response waveform, and a new head portion shape is obtained. For example, a genetic algorithm (GA) may be used as a method of repeatedly calculating the pressure waveform by moving the origin position of each unit response along the X axis so that an ideal pressure waveform can be obtained. Alternatively, a simulated annealing (SA) method may be used.

  In the optimization automatic program according to the present embodiment, the optimization is performed by obtaining the moving direction and moving distance of the point (target point) that is the moving target among a plurality of such unit responses on the surface of the head shape. At this time, by differentiating the unit response, a change in waveform per unit distance that moves the origin of the unit response at the target point in the x direction is expressed. Therefore, the optimal moving direction and moving amount are determined based on the differential value (dr / dX) for the unit response of the target point. Specifically, it is obtained by the following arithmetic expression. In addition, although it demonstrates based on approximate formula number 1 here, it can calculate based on the same variation operation also about Formula 9, Formula 11, and Formula 12.

The variation δq (X) of the pressure gradient waveform by minutely changing the head portion shape by δu (y, z) is obtained as the integral of the derivative of the unit response as shown by the following equation.

  In order to facilitate the understanding of the derivative of the unit response using mathematical formulas, the procedure for the simplified shape shown in FIG. 11 will be described. Here, an example is shown in which the unit response is not corrected but is performed based on Equation (1).

FIG. 13 examines a policy of correcting the pressure gradient waveform 240 generated by the vehicle head portion outer shape 200 shown in FIG. In the pressure gradient waveform 240, the point 241 is the maximum value. It is clearly the waveform 231 derived from the unit response generated by the representative point 201 that contributes most to the generation of the waveform at this position. However, moving the representative point 201 is not a good idea. Because the point 241 is substantially at the same position as the peak point 236 of the waveform 231, the change in the waveform at this position due to the movement of the representative point 201 is close to zero. In addition, since the representative point 201 exists at the tip of the shape, if the point is moved in the negative direction, the length of the leading portion becomes long, which deviates from the dimensional constraints assumed here. .

  Therefore, attention is paid to the representative point 202. A waveform derived from the unit response when only the representative point 202 is moved to the position of the point 242 by the unit amount in the positive direction of the X axis is a waveform 252. If attention is paid to the difference between the waveform 252 and the waveform 232, the waveform fluctuation amount at this time is lowered in the hatched portion 255 and the waveform is raised in the hatched 256 portion. A waveform 259 is obtained by plotting these differences. The waveform 259 is displayed by shifting the origin in the vertical direction in order to avoid overlapping of lines, and a negative region is indicated by hatching 257 and a positive region is indicated by hatching 258.

  A waveform 259 shows the amount of deformation of the total pressure gradient waveform as an amount per unit movement amount when the representative point 202 is moved minutely in the positive direction of the X axis. In other words, regarding Equation 15, δu represents a displacement that deforms the representative point 201 by a unit amount, and the variation δq (X) at that time is a waveform 259. Obviously, waveform 259 is the inverse of the sign of the X derivative of waveform 232. Therefore, in order to decrease the value of the point 241, the waveform 259 is negative at the X coordinate position of the point 241, and therefore the representative point 202 may be moved in the positive direction. When the waveforms 233 and 234 are observed, it can be seen that the movement of the representative point 202 is the best solution if it is deformed by the same amount.

Next, FIG. 14 shows a head shape and a pressure gradient waveform after the representative point 202 is moved as a target point through the consideration shown in FIG. The original representative point 202 moves in the positive direction of the X axis by the amount indicated by the vector 261, and the position of the new representative point becomes the point 262. As a result, the new head portion shape becomes the head portion outer shape 260. Then, since the waveform derived from the unit response of the representative point 262 is the waveform 272, the pressure gradient waveform generated by the entire vehicle is a waveform 280 that is the sum of the waveforms 231, 272, 233, and 234. Therefore, the new waveform 280 has a peak point 281 and a point 282. Therefore, in the waveform 280, the maximum value of the pressure gradient waveform could be lowered as compared with the point 241 of the waveform 240 shown in FIG.

Thus, if the direction and amount of movement of the target response of the target point in the X-axis direction are determined so as to improve the pressure waveform, the surface coordinates of the corresponding head shape can be changed by an amount equal to the amount of movement. The amount of deformation is desirable. The direction of movement is determined by the sign of the value obtained by differentiating the impulse response of the target point at the position where the waveform is to be improved with respect to the X coordinate. Here, the direction of the vector 261 is that. Since Equations (14) and (15) are linearization equations on the assumption that the amount of deformation is very small, the size of the vector 261 is not obtained by a single movement operation, but does not deviate from the assumption of linearization. Repeat the small deformation of and select one that has an excellent pressure waveform.

By the way, the peak values of the point 281 and the point 282 are almost the same, and if the representative point 262 is moved further to the right, the peak on the point 282 side becomes higher this time, so only one representative point is operated. This is the limit for waveform improvement. Therefore, even if the waveform is improved by focusing on only one point on the pressure gradient waveform, the pressure gradient value at other points on the waveform becomes large. Therefore, the magnitude of the vector 261 shown in FIG. 14 is balanced with the value of the peak point 282 that has been deteriorated at that time by repeating minute deformation so as to improve the value of the peak point 281 of interest. Determined. Moving the unit response will alleviate one part of the waveform and worsen the other part. Therefore, it is necessary to try to improve the waveform by focusing on a wide section on the waveform in the waveform close to the optimum shown in FIG. 12 or FIG. There is a need for a method of moving all unit response waveforms in a balanced manner, rather than using only one unit response as a target point. The method is described below.

  Consider an arbitrary pressure waveform θ (X) as a “preferred waveform”. In order to reduce the maximum value of the pressure gradient, it is preferable that the top of the pressure waveform has a substantially trapezoidal shape close to the horizontal, and the rise and fall are steep. Therefore, for example, with respect to the pressure waveform of the pattern 11 shown in FIG. 12, while reducing the values of the peaks P1 and P2, the valley T is raised so that the pressure waveform as shown in the pattern 14 is obtained. In this example, θ (X) is the pattern 14. For this purpose, the head shape shown in FIG. 1 is used as a base, and a head shape that outputs a pressure waveform as shown in the pattern 14 is created.

  In determining the “preferred waveform”, the top may be simply horizontal. For example, the waveform with the top being horizontal is shifted by an amount corresponding to an error that the waveform 702 deviates from the waveform 701 shown in FIG. May be used. Instead of the waveform 701, a waveform measured in an actual tunnel may be used. Thereby, the error by this method can be compensated. In addition, it is possible to add a device so as to reversely correct the waveform undulation that tends to occur in the optimization process. In addition, the pressure waveform generated at the time of entry is deformed by a non-linear effect while propagating in the tunnel. If the deformation due to the non-linear effect worsens the tunnel micro-pressure wave, the tunnel is offset to cancel the effect. The waveform at the time of entry may be designed and set.

More specifically, the difference E from the preferred pressure waveform is squared, multiplied by the weight w in an arbitrary evaluation interval and integrated to obtain a residual E, and the residual E is minimized to obtain an optimum shape. To.
[Ξmin, Ξmax] is arbitrarily set so as to include the top of the waveform in the evaluation section of the waveform on the X axis. In the example of FIG. 12, the section from −0.8 m to 8.4 m is set as the evaluation section.

A minute correction v (y, z) is added to the current shape u (y, z) to make u (y, z) + v (y, z) a new shape. V (y, z) that minimizes the residual E is the solution.

Variation of residual E is
From the condition that this becomes zero for an arbitrary δv (y, z), the equation that the displacement v (y, z) should satisfy is

Discretize the optimization process. The residual E is evaluated with weights wi at N evaluation points on the pressure waveform. i is a subscript.
However, Xi is an evaluation point of discretization, and qi = q (Xi), θi = θ (Xi), and i is a subscript.
The deformation distribution is represented by a linear combination of M arbitrary shape functions hj (y, z). j is a subscript.

Then, simultaneous equations for the diameter number cj are obtained from dE / dcj = 0.
Or it becomes like the following formula which made it easy to understand that it is a linear simultaneous equation.
However, i and j are subscripts,
aij = ∫∫wi {dr (Xi-u (y, z)) / dX} hj (y, z) dydz
Integral fi at {y, z) εσ = { qi−θi } wi
Here, aij represents a matrix, cj represents an optimum displacement coefficient, and fi represents a residual.

  Therefore, basically, this equation is solved to output the head portion shape. As a result of the investigation, it was found that the number of equations 23 is extremely singular. It is an inverse problem in nature and is presumed to be due to the nature of including the inverse transformation of the unit response. For the same reason, even if the steepest descent method or the common benefit gradient method is performed using the gradient shown in Equation 15, convergence is poor. For this reason, a least squares solution is obtained by singular value decomposition, which is a practical solution. Of the singular values that appear in the diagonal component due to singular value decomposition, the one with the smallest absolute value is cut off for calculation. Otherwise, the shape will be extremely uneven. Then, the solution cj obtained here shows how the shape is deformed in order to minimize the square of the error from the desired pressure waveform in order to make the head portion the optimum shape.

The shape function used in Equation 21 is a candidate for how to optimally move the unit response. The selection is arbitrary, but in particular, it is efficient to include the component dr (Xi-u (y, z), y, z) / dX and satisfy the dimensional constraint condition. This is because dr (Xi-u (y, z), y, z) / dX and components proportional thereto are each point on the yz projection plane that changes the value of the point of Xi on the waveform in the positive direction. the amount of movement of the distribution in the x direction because indicates both the magnitude of the sensitivity of such a movement pattern is a good candidate to improve the waveform.

  In addition, there are dimensional boundary conditions that must be satisfied in advance, the point that must be fixed, and the distribution of dr (Xi-u (y, z), y, z) naturally tries to break the inequality constraint condition on dimensions. If the component corresponding to the point that has obvious properties is previously set to 0 or a minute value, a solution satisfying the dimensional constraint condition can be obtained in the least square solution. One effective way to mitigate the maximum pressure gradient is to increase the length of the vehicle head, so if there are candidates that can break the dimensional requirements, the least squares solution will naturally Only the solutions to increase the length of are shown. After obtaining such a solution, if the deformation amount is forcibly adjusted to satisfy the dimensional constraint condition, the pressure waveform is deteriorated. In other words, it is desirable to consider the dimensional constraint conditions when selecting the shape function before solving the simultaneous equations.

  Since the optimal solution described here is the result of linearization, it is desirable to limit the maximum amount of movement so as not to deviate from the approximation of linearization when making a minute change. For example, the movement amount is scalar multiplied so that the maximum movement amount is about 100 mm at maximum with respect to the obtained displacement vector, and the shape is corrected while repeating the movement within the range.

As an example showing how to select a shape function, an example is shown in which M = N and variation at the target point is selected as the shape function.

Here, FIG. 15 is a diagram in which the base shape of FIG. 1 is overlapped with the optimal shape obtained by optimizing the top shape, and the surface of the base shape is represented by a mesh, and the optimal shape is expressed as a volume. It is expressed by a solid line. The portion where the mesh disappears indicates that the surface has risen more than the base shape by optimization, and conversely, the portion where the gap is formed indicates that the surface is recessed. Specifically, the bulge of the cart cowl portion 21 extends forward, and as a result, the local cross-sectional area change rate at the cowl portion is reduced, while the width is reduced at the upper portion 27 of the cart cowl, and the shoulder portion 22 is swollen by swelling the surface, also become blunt so as to flatten the tip portion 23 of the nose groove 24 between the tip 23 and the distal end portion 26 which is divided vertically is deeper rearward cab portion 25 The roof was shown to be lower.

  The pressure waveform obtained for the head shape optimized in this way is a pattern 12 shown in FIG. In this pressure waveform, the peaks P1 and P2 and the troughs T of the pattern 11 disappeared, the top portion was substantially trapezoidal, and the rise and fall were steep and approached the ideal pattern 14. 16 is a perspective view showing the shape of the head portion of the pattern 12 in which the shape of the head portion of FIG. 1 is optimized. FIG. 17 is a contour line of the three-dimensional shape of the head shape shown in FIG. It is the figure shown by. Further, FIG. 18 is a perspective view showing a head shape optimized similarly based on another base shape. FIG. 19 is a diagram showing the three-dimensional shape of the head shape shown in FIG. 18 as a contour line when viewed from the front, and the pattern 13 shown in FIG. 12 is obtained by the pressure obtained by the head shape of FIGS. It is a waveform.

  Therefore, the head shape optimization automatic program makes it easy to create a head shape optimized to reduce micro pressure waves based on the design-oriented head shape created by the designer, for example. I was able to do that. In addition, the optimization process can be performed in a few tens of minutes, and the head shape can be provided with a very fast response.

  Note that this automatic optimization program for the head shape is such that the optimum shape shown in FIG. 16 and FIG. 18 thus obtained necessarily satisfies the constraint conditions other than the micro-pressure wave to be satisfied as the shape of the vehicle head part. is not. That is, the optimization automatic program according to the present embodiment exerts an effect as a solver for deriving an optimal solution suitable for the condition related to the micro-pressure wave reduction.

  By the way, the impulse response obtained corresponding to the cross section of the head shape has a sharp peak value appearing at the sample point 3 shown in FIG. 5 or a peak value such as the sample points 13, 18, and 23. It differs depending on each cross-sectional position, such as a low and wide appearing in the x direction. The sharp impulse response means that the influence of the change in the cross-sectional area of the head shape at the cross-sectional position on the pressure waveform is concentrated locally. Therefore, in consideration of such a difference in the influence of the impulse response, a condition for reducing the micro-pressure wave is set in determining the head shape. Note that it is assumed that the shape of the top portion is symmetrical.

  For example, for the impulse response as shown in FIG. 5, the ratio is obtained by integrating before and after X = 0. As a result, whether the unit response obtained at a plurality of positions on the yz plane has a large influence on the vehicle front (X negative area) or on the rear (X positive area) depending on each position. I understand. Therefore, an impulse response that has a large influence on the front of the vehicle acts on the front side of the vehicle as much as possible, while an impulse response that has a large influence on the rear of the vehicle acts on the rear side of the head portion shape that is as close to the general part as possible. It is preferable to disperse in order to obtain the pressure waveform of the pattern 14 shown in FIG.

Regarding the impulse response distribution r (X, y, z) on the yz plane, considering the amount of pressure waveform rising after the origin of X (X = 0), the integral of the following equation is expressed as “Latter Fulfilling” Factor) ”. FIG. 20 shows a numerical example of the rear sufficiency. FIG. 20 shows the rear sufficiency distribution on the yz projection plane on the assumption that the vehicle head shape is symmetrical.

Therefore, when creating the head portion shape, an impulse response indicating a low value of rearward satisfaction is arranged on the front side of the head portion. In this case, “the front side of the head” indicates a range of x <0.5R, where R is a radius of a circle having the same area as the tunnel cross-sectional area. This is because it is reasonable to measure the impulse response because it is proportional to R. In the Shinkansen tunnel, it is approximately R = 4.4m. In this specific example, “the front side of the head” refers to a range from the tip to 2.2 m.

Next, regarding the distribution r (X, y, z) of the impulse response on the yz plane, considering the amount that the pressure waveform rises in the negative region of X, the integral of the following equation is expressed as “Former Fulfilling” Factor) ”.

  There is a non-overlapping region in each integration interval of the rear sufficiency and the forward sufficiency, and it is not symmetrical with respect to the origin, but this is a strong asymmetry about the X axis in the impulse response as shown in FIG. Focusing on the fact that the center of gravity of the waveform is in the vicinity of -0.5R, which is the middle of the section of -R <X <0 corresponding to the section between the integration sections, such an index is used. . FIG. 21 shows a numerical example of the front sufficiency, and shows the front sufficiency distribution on the yz projection plane on the assumption that the vehicle head shape is a symmetrical shape.

Therefore, in creating the head portion shape, an impulse response indicating a low value of the front sufficiency is arranged on the rear side of the head portion. In this case, “the rear side of the head portion” indicates a range of L−0.5R <x <L, where R is a radius of a circle having the same area as the tunnel cross-sectional area and L is a length of the head portion.

  As described above, as a result of obtaining the front sufficiency and the rear sufficiency, it is preferable that the front end portion of the nose is formed in a flat shape as shown in FIG. I understood. Therefore, in creating the head portion shape, it is preferable that the height of the center of gravity of the nose cross section formed in a flat shape is in the range of 1000 mm to 1800 mm from the upper surface of the rail.

  Further, as a result of obtaining the front sufficiency and the rear sufficiency, on the rear side of the head portion, a region obtained by subtracting the cross section at the x coordinate position from the cross section of the vehicle of the general portion (the rear portion is satisfied from the x coordinate depicting the cross section). It is preferable that the height of the center of gravity of the region is 2600 mm or more and 4500 mm or less from the upper surface of the rail.

  By the way, since the impulse response has a sharper waveform as it is closer to the side surface of the tunnel, it is not preferable to form a shape that gives a large cross-sectional area change to the side surface portion. Since it is a portion close to the tunnel wall surface in the double track tunnel, the unit response waveform is sharpest in the portion close to the maximum width on the yz projection plane as shown in FIG. If the shape has a large local cross-sectional area change rate in this portion, a peak is formed in the pressure gradient waveform. This is because the unit response waveform of the portion other than the portion close to the maximum width is gentler than this, so that it is difficult to correct unevenness on the sharper waveform even if the arrangement of the gentle one is devised. For this reason, when creating the head portion shape, the side surface portion of the vehicle body close to the side surface of the tunnel is required to be as smooth as possible. Therefore, the following design conditions were determined.

Here, the section (0.5R <x <L) excluding the front end side of the head is handled. When the vehicle body width of the head portion shape is b, the vehicle body is divided into four equal parts in the width direction (y direction) at any position within the section of the x coordinate of the head portion shape , and these are further divided by -b <y < It is divided into three regions: -0.5b (left end: 1/4), -0.5b <y <0.5b (center: 1/2), and 0.5b <y <b (right end: 1/4). Further, the cross-sectional area at the position of x = 0.5R is AF = A (0.5R), the cross-sectional area at the position of x = L is AR = A (L), and the cross-sectional area of the region obtained by adding the left end portion and the right end portion is summed up. Is Aside (x).

Therefore, the design condition is that the maximum value of the cross-sectional area change rate on the side surface side is larger than the average value of the entire cross-sectional area in the section in the section (0.5R <x <L) excluding the front end side of the head portion. In order to avoid this, the following equation is satisfied.

Having described the embodiment for the present invention, without having to be limited to this, Ru der allows various modifications without departing from the spirit thereof.

In the embodiment, the impulse response is a pressure gradient waveform obtained by differentiating the pressure. However, a pressure waveform that is an integral value thereof may be used. That is, the pressure waveform may be stored as an impulse response. Equations 1 to 13 can be used as they are, and r is replaced with “unit pressure response” having a dimension of [pressure divided by area], and q is replaced with “pressure waveform” having a dimension of [pressure]. Even when the pressure gradient is calculated by differentiating the obtained q in the evaluation, the obtained effect is the same as the effect obtained in the above embodiment.
Moreover, in the said embodiment, although the impulse response has shown the thing of speed 300km / h, it can be used about the speed at which a train is actually operated about speed.

  In addition, the impulse response of the embodiment can be obtained in the geometry around the actual tunnel entrance. For example, a cover that has the same shape as the tunnel cross section or larger than the tunnel cross section and is installed at the entrance of the tunnel to prevent noise, snow damage, and earth and sand disasters, a soundproof wall beside the track, and terrain The impulse response database can be used by numerical calculation or experimentally obtained in a state including structures that affect the air flow around the tunnel entrance, such as combined cut and fill. By doing so, the pressure gradient waveform in a state including these structures can be obtained with high accuracy, and a shape for reducing the pressure gradient can be obtained in a state in which these structures are taken into consideration.

  Further, the impulse response of the above embodiment is obtained by arranging tunnel implants at each cross-sectional position, and 25 sample points are provided on the yz projection plane, and numerical calculation for 25 times is performed. If symmetrical conditions are attached, numerical calculation can be performed by placing a total of two driving bodies at both a sample point and a sample point at a symmetrical position across the vehicle center line. In this case, 15 numerical calculations are sufficient.

It is the side view which showed the head part shape of the high-speed rail vehicle. It is an image figure of the tunnel entry calculation which calculates | requires an impulse response. It is the figure which showed the sample point of the impulse response in a yz plane. It is the figure which showed the driving body at the time of calculating | requiring an impulse response. It is the figure which showed the impulse response. It is the figure which showed the three-dimensional shape of the vehicle head part with the contour line which looked at from the front. It is the figure which showed the view of the cross-sectional area response in an axisymmetric model. It is the figure which showed the view of the cross-sectional area response in the three-dimensional model using an impulse response. It is the figure which showed the side view and pressure gradient waveform of a three-dimensional shape about head part shape. It is the figure which showed the example which calculates | requires a pressure gradient waveform by superposition of a unit response. It is the figure which showed the example which calculates | requires a pressure gradient waveform, when a unit response has spatial nonuniformity. It is the figure which showed the pressure waveform calculated | required using the impulse response about each head part shape. It is the figure which showed the example which calculates | requires the variation which a pressure gradient waveform changes when the representative point which comprises a shape is moved minutely. It is the figure which showed the example which moves the representative point which comprises a shape, and improves a pressure gradient waveform. It is the figure which piled up and showed the base shape of FIG. 1, and the optimal shape which optimized it about the head part shape. It is the perspective view which showed only the head part shape which optimized the head part shape of FIG. It is the figure which showed the three-dimensional shape about the head part shape shown in FIG. 16 with the contour line which looked at from the front. It is the perspective view which showed the head part shape optimized based on the other head part shape. It is the figure which showed the three-dimensional shape about the head part shape shown in FIG. 18 with the contour line which looked at from the front. It shows a backward sufficiency distribution on the yz projection plane. It shows the forward sufficiency distribution on the yz projection plane. It is the figure which showed the pressure gradient distribution of the compression wave produced by a different head part shape.

Explanation of symbols

10 Driving body

Claims (8)

The shape of the leading part from the tip of the high-speed railway vehicle to the position in the traveling direction where the cross section perpendicular to the traveling direction is maximum is specified in three dimensions, and the arbitrarily created high-speed railway vehicle with the leading part shape enters the tunnel. It is a method to obtain the pressure waveform generated when
The impulse response of the pressure wave caused by the change in the cross-sectional area of the unit amount is obtained at a plurality of positions representing an arbitrarily subdivided region on the yz projection plane orthogonal to the x axis in the vehicle traveling direction, and the impulse response is stored in the database. Save as
A high speed characterized in that the arbitrarily created head shape is summed by convolution integration of the area cross-sectional area change rate for each subdivided region of the head shape and the corresponding impulse response of the database. A method for obtaining a pressure waveform for the shape of the top of a rail vehicle. The shape of the leading part from the tip of the high-speed railway vehicle to the position in the traveling direction where the cross section perpendicular to the traveling direction is maximum is specified in three dimensions, and the arbitrarily created high-speed railway vehicle with the leading part shape enters the tunnel. It is a method to obtain the pressure waveform generated when
Obtaining an impulse response of a pressure wave caused by a change in cross-sectional area of a unit amount at an arbitrary plurality of positions on a yz projection plane orthogonal to the x axis in the vehicle traveling direction, and storing the impulse response as a database;
An impulse response representing the coordinates (y, z) is expressed as a function as r (X, y, z) based on the database, and the x coordinate of the outer surface of the head shape at the coordinates (y, z) is represented by u ( y, z) as a function, and in a region σ where the vehicle exists when the vehicle is projected onto the yz plane,
A method for obtaining a pressure waveform for a top shape of a high-speed railway vehicle, wherein the pressure waveform q (X) of the arbitrarily created top shape is obtained by performing integral calculation. The shape of the leading part from the tip of the high-speed railway vehicle to the position in the traveling direction where the cross section perpendicular to the traveling direction is maximum is specified in three dimensions, and the arbitrarily created high-speed railway vehicle with the leading part shape enters the tunnel. It is a method to obtain the pressure waveform generated when
Obtaining an impulse response of a pressure wave caused by a change in cross-sectional area of a unit amount at an arbitrary plurality of positions on a yz projection plane orthogonal to the x axis in the vehicle traveling direction, and storing the impulse response as a database;
An impulse response representing the coordinates (y, z) is expressed as a function as r (X, y, z) based on the database, and the x coordinate of the outer surface of the head shape at the coordinates (y, z) is represented by u ( y−z) as a function, where A (x) is the area surrounded by the vehicle body outline obtained by cutting the head shape at the position of the coordinate x, and S− is the cross-sectional area of the tunnel. In the region σ where the vehicle exists when the vehicle is projected on the z plane,
A method for obtaining a pressure waveform for a top shape of a high-speed railway vehicle, wherein the pressure waveform q (X) of the arbitrarily created top shape is obtained by performing integral calculation. In a method for obtaining a pressure waveform for a top shape of a high-speed rail vehicle according to any one of claims 1 to 3,
The impulse response at a position on the yz projection plane other than the impulse response stored in the database is obtained by interpolation from the impulse response stored in the database. How to find the waveform. A method for optimizing the shape of the leading portion of a high-speed railway vehicle whose pressure waveform is obtained by the method according to any one of claims 1 to 4,
The procedure for changing the pressure waveform by moving the origin position of the impulse response waveform from which the pressure waveform was derived along the X axis is performed a plurality of times, and the pressure waveform obtained by the plurality of procedures is more excellent. Selecting a pressure waveform indicating a value and displacing the shape of the vehicle surface by an amount corresponding to the amount of movement of the impulse response waveform in the selected pressure waveform to obtain a new head shape Optimization method. In the optimization method of the head part shape according to claim 5,
The movement of the impulse response along the X axis is obtained by squaring the difference between the preferable pressure waveform and the pressure waveform, and integrating it in the evaluation section on the arbitrarily set waveform. A method for optimizing the shape of the head part, characterized in that it approaches zero. In the optimization method of the head part shape according to claim 5 or claim 6,
When the impulse response moves along the X axis, the impulse response is differentiated with respect to the X coordinate, and an optimum moving direction and amount of movement are obtained based on the differential value. Method. A head shape of a high-speed railway vehicle, which is obtained by using the method for optimizing a head shape according to any one of claims 5 to 7.