JP2003034819A - Apparatus for heat treating steel plate - Google Patents

Abstract

PROBLEM TO BE SOLVED: To provide an apparatus for heat treating steel plates with the use of an induction heating device of high efficiency, which uniformizes temperature distribution across short transverse and long transverse directions, and does not cause defects in quality by setting an upper limit to the surface temperature. SOLUTION: The apparatus for heat treating the steel plates which disposes several solenoid type induction heating devices (hereafter referred to as inductors) in series, is characterized by setting the upper limit for quantity of raising temperature on each inductor, so that the surface temperature of the steel sheet may not exceed the target upper limit temperature which is lower than the magnetic transformation temperature (Curie temperature).

Description

Detailed Description of the Invention

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to a thick steel plate to which a solenoid type induction heating device suitable for rapid heating is applied, which is more efficient than the conventional atmosphere heating furnace in the heat treatment process of quenching, annealing and tempering of a heat treated steel plate. The present invention relates to a heat treatment apparatus.

[0002]

2. Description of the Related Art When an induction heating apparatus suitable for rapid heating is applied to a heat treatment process such as quenching, annealing, and tempering of a thick steel plate, some objects due to the fact that objects to be heated except stainless steel are ferromagnetic materials at room temperature. It is necessary to solve that problem. That is, to uniformly heat the thickness distribution and the temperature distribution in the width direction. That is, minimize the temperature difference between the center of thickness and the surface. When the temperature is not uniform, the quality of heat treatment is greatly affected. Do not exceed the target upper temperature limit during the heating process. When the target upper limit temperature defined above is exceeded, precipitation of additive elements in the steel occurs and the quality is affected. At the same time when the magnetic transformation point is exceeded, the penetration depth increases and heating efficiency deteriorates. Select the optimum heating frequency for the induction heating device within the range of the thickness of the material to be heated. This has a great influence on the uniformity in the plate thickness direction, the soaking property for preventing edge overheating, the heating efficiency and the productivity.

Japanese Unexamined Patent Publication (Kokai) No. 48-25237 discloses a measure for preventing temperature nonuniformity at the front and rear ends in the longitudinal direction of the plate when a plurality of solenoid type induction heating devices are arranged in series.

Further, Japanese Unexamined Patent Publication (Kokai) No. 48-64534 discloses that if heating is performed at a Curie point or lower, it is possible to uniformly raise the temperature of a material having a non-uniform thickness by alternating heating of low frequency induction heating and high frequency induction heating. Has been done.

[0005]

However, the above-mentioned conventional technique has the following problems.

Japanese Unexamined Patent Publication (Kokai) No. 48-25237 does not describe the viewpoint of preventing plate deformation due to heating strain and the temperature nonuniformity in the plate thickness direction, and the heat treatment of the entire plate cross section cannot be performed uniformly.

Further, in JP-A-48-64534, if the heating is performed at the Curie point or lower, it is possible to uniformly raise the temperature of the material having a non-uniform thickness by the alternating heating of the low frequency induction heating and the high frequency induction heating. However, if the material to be heated has a small thickness, there is a problem that the temperature cannot be sufficiently raised. This is about 50-20
In the case of low-frequency induction heating near the commercial frequency of 0 Hz, as shown in the following formula (1), the heat input power decreases in proportion to the frequency, and it is necessary to take an enormous amount of current in order to obtain a sufficient magnetic field. If the heating frequency is low, there is a lower limit of the plate thickness that can be heated (for example, when the heating frequency is 200 Hz, the lower limit is about 17 mm). This technique makes it difficult to heat treat steel plates having various thicknesses.

P = π · μ · f · H 2 · S · L · Q (1) where P: heat absorption power, μ: permeability, f: frequency,
H: magnetic field strength, S: material cross-sectional area, L: material length, Q: absorption coefficient.

The object of the present invention is to solve the above-mentioned problems of the prior art, to make the temperature distribution in the plate thickness and plate width direction uniform using a highly efficient induction heating device, and to add a surface temperature upper limit. Accordingly, the object is to provide a heat treatment apparatus for thick steel plates that does not cause quality defects.

[0010]

That is, the heat treatment apparatus for a thick steel plate of the present invention has the following features.

(1) In a heat treatment apparatus for a thick steel plate in which a plurality of solenoid type induction heating devices (hereinafter referred to as inductors) are arranged in series, the steel plate surface temperature does not exceed a target upper limit temperature below a magnetic transformation point (Curie temperature). As described above, the heat treatment apparatus for a thick steel plate is characterized by setting the single unit temperature rise amount of each inductor.

(2) The heat treatment apparatus for a thick steel plate according to claim 1, wherein after the surface temperature is lowered between the inductors, intermittent heating is performed by heating with the next inductor.

(3) The thick steel sheet according to claim 1 or 2, characterized in that the distribution of input power of each inductor is changed so that the average temperature of the thick steel sheet on the output side of each inductor satisfies the target value. Heat treatment equipment.

(4) The heating frequency of each inductor is set to 20
The frequency is set to 0 Hz to 2000 Hz.
4. The heat treatment apparatus for a thick steel plate according to any one of 1 to 3.

(5) The single unit temperature rise of each inductor is set to 40
The heat treatment apparatus for a thick steel plate according to any one of claims 1 to 4, wherein the temperature is 0 ° C or lower and three or more inductors are arranged in series.

(6) The coil length of each inductor is 1.
The heat treatment apparatus for a thick steel plate according to any one of claims 1 to 5, which has a length of 5 m or less.

(7) The inductors are arranged at a distance of 300 mm or more from each other.
The heat treatment apparatus for a thick steel plate according to any one of 1.

[0018]

BEST MODE FOR CARRYING OUT THE INVENTION A heat treatment apparatus for a thick steel plate in which a plurality of solenoid type induction heating devices (hereinafter referred to as inductors) of the present invention are arranged in series has a target upper limit of a steel plate surface temperature equal to or lower than a magnetic transformation point (Curie temperature). The single unit temperature rise of each inductor is set so that it does not exceed the temperature. If the steel plate surface temperature exceeds the target upper limit temperature during the heating process, precipitation of additive elements in the steel will occur and the quality will be affected, and if the magnetic transformation point is exceeded, the penetration depth will increase and the heating efficiency will deteriorate. is there.

The requirement of the present invention is to optimize the heating power distribution of a plurality of solenoid-type inductors arranged in series and the passage time (soaking time) between the inductors, and particularly for a thick material (plate thickness 14 mm The above is to make the temperature in the plate thickness direction uniform. Thin materials are more likely to diffuse heat than thick materials, and soaking conditions are more advantageous than thick materials.

The preferable conditions of the heat treatment apparatus for a thick steel plate capable of making the temperature distribution in the plate thickness direction uniform within these ranges are as follows. Set the temperature rise of each inductor to 400 ° C or less, and arrange three or more inductors in series. The heating frequency of each inductor is 200Hz-2000
Be Hz. Place each inductor at a distance of 300mm or more. The coil length of each inductor is 1.5 m or less. In order to equalize the temperature in the plate thickness direction, a plurality of inductors arranged in series and the distance between the inductors are separated by 1 to 20 seconds in terms of transit time, and heating power distribution with a high degree of soaking, that is, strong heating of the preceding inductor, is achieved. To use. To prevent surface overheating, the amount of temperature rise per inductor is specified, and the distance between inductors is calculated as 1 in terms of transit time.
The surface temperature can be lowered within the soaking time of 20 seconds to 20 seconds, and intermittent heating is performed by heating with the next inductor.

The grounds for solving the problems will be shown below. [Heating method based on surface temperature rise and concept of distance between inductors] It is necessary to arrange at least three inductors in series. The basis of the number of inductors and the heating control method is shown below.

Necessity of heating method based on upper limit of surface and plate edge temperature In heat treatment of thick steel plate, it is conceivable to heat up to 650 ° C., for example. This heating is generally known as heat treatment for the purpose of stress relief. This is a process in which carbon steel is heated in the range of 450 ° C. to 650 ° C. and then gradually cooled or air cooled. At this time, if it is heated to 650 ° C. or higher, there arises a problem that the mechanical strength is lowered, and if there is temperature unevenness in the plate thickness and the plate width direction, there is a problem that the stress release becomes uneven. Therefore, also in the heating process, it is necessary to strictly adhere to the upper limit of the surface temperature for heating. This means that high power cannot be applied to the latter part (high temperature range) of the inductor.
As described above, in the heat treatment of the thick steel plate, it is preferable to change the distribution of the input power of each inductor by performing the first-stage strong heating and the second-stage weak heating.

Relationship between Upper Surface Temperature Upper Limit Heating and Distance Between Inductors Next, consideration will be given to securing a soaking time (uniformization of surface and central temperature). Because of the principle of induction heating, it is necessary to secure a longer soaking time for a thick material (plate thickness 14 mm or more), so we will focus on thick materials. Moreover, from the principle of the previous stage strong heating,
Alternatively, the soaking time of the second heating inductor can be adjusted to a plate thickness of 8 mm.
-50 mm material is compared. FIG. 3 is a comparison of required soaking time for each plate thickness of thick steel plates and passage time between induction heating devices for thick steel plates when heated at the same efficiency. In determining Fig. 3,
The following constants for calculation were used. Air-cooling emissivity ε: 0.78, average thermal conductivity λ: 37 (kcal /
mh ℃), average density ρ: 7800 (kg / m3), average specific heat Cp:
0.132 (kcal / kg ℃) (0.16kcal / kg = 670J / kg is 100 ℃
According to this, it takes about 20 seconds to soak a plate having a thickness of 50 mm. Therefore, when the plate is passed at 3.5 mpm, 1.15 m
It is necessary to secure the distance between the inductors. Also,
18 mpm because it is necessary to secure about 1 second for soaking 8 mm material
In case of passing through, the distance between the inductors should be 0.3 m or more. Therefore, each inductor is 300mm
It is preferable to dispose the above distance.

Since the soaking time has a monotonically increasing relationship with the temperature rise amount per inductor, the distance between the inductors is defined from the soaking time, and the temperature rise amount is further defined. In this case, if the temperature rise amount of the single machine is 400 ° C. or less, a thick steel plate up to 20 mm can be heated with high efficiency by ensuring a space between the inductors of 0.65 m or more. Also, if the inductors are separated by 1.15m, 50
A thick steel plate up to mm can be heated with the same efficiency as a 20 mm material.

Grounds for requiring three or more inductors Inductors input energy from the surface of the material to be heated, which is in principle inconsistent with uniform heating. Therefore, when aiming at soaking, the heating inductor should have soaking characteristics as much as possible while having the soaking process as described above.

Although it is desired to make the inductor length as long as possible and have a uniform heating characteristic, the roll interval at which the thick steel plate can be supported by the roll is 1.5 m, which is the limit at which the steel plate strikes the flexible roll. It is preferable to limit the length to 5 m or less.

The maximum possible temperature rise amount in the limit inductor length (coil length) is practically 400 ° C. as a limit. Plate thickness 20mm, plate width 4500mm, inductor passing speed 0.6mpm, inductor length 1.5m, maximum temperature rise per inductor when heating inlet temperature 20 ℃ (normal temperature) to target temperature 650 ℃ About 4
The limit was 00 ° C. This is because the plate edge temperature rises by about 1.5 times the plate center temperature when heated at a commercial frequency or higher, and FIG. 4 shows the temperature rise relationship. The basis of the inductor passing speed is the speed when induction heating is performed at an equivalent efficiency of 25 T / H of the gas-fired furnace.

From such a study, 630 ° C. (650-2
0) Considering the temperature rise, the heating inductor is 630/4
Since 00> 1, two or more inductors are required. Further, considering the heating plan with the uniform heating condition that the plate edge temperature is less than the target upper limit temperature as a constraint condition, when the edge temperature constraint of the first inductor 630 ° C. = 1.5 × θ1 (first inductor average temperature rise amount), θ1 = 420 ° C The required temperature rise after the second inductor is 630-420 =
210 ° C. Edge temperature restriction of the second inductor 210 ° C. = 1.5 × θ2 (average temperature rise of the second inductor) θ2 = 140 ° C. The required temperature rise after the third inductor is 210-140 =
70 ℃ Third inductor edge temperature constraint 70 ℃ = 1.5 × θ3 (third inductor average temperature rise)
Therefore, the sum of θ3 = 47 ° C. θ1 to θ3 is 607 ° C. Therefore, in the case of 630 ° C. temperature increase, it is preferable that the single machine temperature increase amount is 400 ° C. or less and at least three inductors or more.

Further, this problem can be treated as a general optimization problem, and is formulated, for example, in the equation (7).

That is, the average heat-up temperature θi (i = 1, n) after soaking at the outlet of each inductor, the target average heat-up temperature θr
ef, deviation Ki between the average temperature at each inductor outlet and the plate edge temperature Ki (i = 1, n), heating efficiency ηi (i = 1, n)
Then, θ1 + θ2 + ... + θn = θref (Balance of heat-up temperature) Σθi-1 + Ki <θmax (upper limit temperature constraint) J = Σω ・ (θmax-Σθi-1-Ki) ² → min (Temperature deviation Minimization (7) This is a general optimization problem that can be easily solved by mathematical programming, and it can be seen that a heating plan can be established by this mathematical formula. Can reach a wide temperature range.

[Concept of frequency selection] The heating frequency is set to 2
The uniform heating effect is small even in the vicinity of the commercial frequency of less than 00 Hz.

The temperature difference in the plate thickness direction is defined by the following formula.

Δθ = θs−θc (2) Δθ: temperature difference between surface and center, θs: surface temperature, θc: center temperature Further, Δθ is calculated under the heating condition according to the equation (3).

Δθ = F · p · t / k (3) Here, F is a coefficient indicating the degree of temperature difference generation, p is the heat absorption power per unit area of the cross section, P / (W · L) (P:
Heat absorption power of the equation (1), S: material cross-sectional area = t · W),
t: material plate thickness, W: material width, k: thermal conductivity.

Now, in order to reduce Δθ within a possible range,
There are (a) a method of making F small and (b) a method of making p small, and both will be examined.

(A) A method of reducing F.

[0037]   Relationship between penetration depth δ and plate thickness t χ = t / δ (4) When expressed using, F is expressed by equation (5).

F = 1- (W-1) / χ / Y (5) W = 1/2 ・ (cosh (χ) + cos (χ)) Y = sinh (χ) -sin (χ) Becomes FIG. 1 shows the relationship between F and χ when heating is started from about 20 ° C. near room temperature based on equation (5).

The resistivity ρ near 600 ° C. of the ferromagnetic material is 75
(μΩ · cm), relative permeability μ around 600 ℃ is heating frequency 1
15 at 00 Hz, 3 at heating frequency 1500 Hz
2, the penetration depth δ is 2.0 mm <δ <11.2 mm when the heating frequency f is in the range of 100 to 1500 Hz.
Therefore, if the plate thickness is 30 mm, χ is 2.7 <χ <1.
It will be 5.0. At this time, the range of F is 0.88 <F <0.
Therefore, even if the frequency f is reduced 1/15 times, the effect of reducing F is only about 9%. Since this heating device is for heating the magnetic region of steel, the penetration depth is originally small,
It can be seen that even if the heating frequency f is significantly reduced, the effect of reducing F, which is a coefficient indicating the degree of temperature difference, is extremely low.

(B) A method for reducing p.

Since the heat absorption power p per unit area of the cross section is the energy for temperature rise, it suffices to define p sufficiently small considering only the temperature difference minimization, but the number of inductors increases and the inductor length increases. The problem arises. In addition, the problem that the loss due to air cooling and removal increases as the number of devices increases and the heating efficiency lowers cannot be ignored, and p cannot be simply lowered. If p is lowered, it is necessary to lengthen the inductor length. Therefore, while maximizing the heating capacity of the inductor device,
Limited thickness range (heat treated thick steel plate is 8mm-50mm)
It is necessary to find out the single unit temperature rise amount that achieves uniform heating.

The heat absorption power p per unit surface area is expressed by the equation (6).

P = π · μ · f · H2 · t · Q (6) where p: heat absorption power per unit area, f: heating frequency, H: magnetic field strength, μ: transmission Magnetic susceptibility, Q: Power absorption coefficient.

When the basic equation of induction heating is derived from Maxwell's equation, ∇2 H = μ / ρ · ∂H / ∂t
Therefore, FIG. 2 shows the change in Q obtained under the conditions related to the flat plate (widthwise infinity condition).

It can be seen that the transition of Q with respect to χ = t / δ is about 1/6 in the range of χ obtained in the previous section (2.7 <χ <15.0). Therefore, when p is determined in the equation (6), if 1500 Hz is selected, the heating frequency f is 15
Since it is doubled, it is not necessary to take a large magnetic field strength H. Taking a large magnetic field H means that the magnetomotive force of the inductor
The magnetic flux density is also increased, which increases the difficulty in designing the entire device.

On the other hand, the heating frequency is 10 as shown above.
Since it is easy to change the frequency more than twice, it is possible to obtain high heat absorption power by increasing the frequency.
Here, the absorbed power when heated at 60 Hz and 600 Hz is compared. Χ is calculated with the thickness of the heating material being 30 mm and the relative permeability μ near 600 ° C. being 12 and 25 respectively when heated at 60 Hz and 600 Hz, and the resistivity ρ near 600 ° C. being 75 (μΩcm). Then, when heating at 60 Hz, δ = 16.2 mm, χ = 30 mm
/ 16.2 = 1.9 600Hz heating, from δ = 3.6mm, χ = 30mm
/3.6=8.3 f × Q is proportional to the amount of heat input, so comparing the values of f × Q, f × Q = 60 × 0.3 = 18 at 60 Hz, f × Q at 600 Hz = 600 × 0.12 = 72 or more As described above, by setting the heating frequency to approximately 10 times the commercial frequency, it is possible to obtain nearly four times the absorbed power.

At present, the upper limit of the frequency at which an output of several thousand KW can be obtained is about 1500 Hz, so at least 200 Hz.
The above heating causes no problem in terms of device technology. From the above, it is necessary to increase the heating frequency with an emphasis on securing the heat absorption power, and at the same time, it is necessary to reduce the heat absorption power p within the range in which the inductor length can be extended in order to reduce the temperature difference. . (P = P / (W · L), so L = 0.3 m and L = 1.5 m are 5 times different. Also, the limit of the roll interval of the thick plate is 1.5 m on the threaded plate, The inductor length limit is 1.5 m.) When the heating frequency is 200 Hz to 2000 Hz, the heating capacity is secured and a uniform heating effect is also obtained.

Χ = t / δ = 2.3 which is the Q value peak in FIG.
If the χ value becomes smaller, the heating efficiency is significantly reduced, and therefore, if the heating frequency is less than 200 Hz, it is impossible to heat a thin material (thickness less than 14 mm). That is, when the heating frequency is low, there is a lower limit of the plate thickness that can be heated. (For example, when the heating frequency is 200 Hz, the lower limit value is about 17 mm.) When the heating frequency is 200 Hz to 2000 Hz, it is possible to uniformly heat a thin material to a thick material (sheet thickness 14 mm or more), which is preferable.

On the other hand, when the heating frequency exceeds 2000 Hz, in the case of a thick material, the heating frequency is 200 Hz to 2000 H.
The temperature rise amount at the edge is higher than that at z. This is because when the heating frequency exceeds 2000 Hz, the penetration depth δ
The ratio (χ value) between the plate thickness and the plate thickness becomes small, and there is also a sneak current in the corners of the thick steel plate, and the heating along the corners becomes significant and the overheating of the edges increases, but the heating frequency is 20
This is because at a frequency of 00 Hz or less, the corner current becomes small and heating is stopped.

As described above, when the material to be heated is made uniform in the plate thickness direction, low frequency heating (heating frequency of about 200) is required.
It is understood that (Hz or less) is not necessary.

[0051]

[Example] The heat treatment of a thick steel plate having a plate thickness range of 8 to 50 mm and a plate width of 4600 mm was carried out at a heating efficiency of 390 T / H. The specifications of the heat treatment apparatus are as follows. The heating frequency of each inductor is 1000 Hz. Set the single unit temperature rise of each inductor to 400 ° C or less, 3
Place more than one inductor in series. The coil length of each inductor is 1.2 m. Each inductor is placed with a distance of 650 mm.

Example 1 In the example of the present invention, the plate thickness 1 is shown in FIG.
For 2 mm thick steel plate, using the inductor of the above specifications, when heating from 20 ° C to 650 ° C and raising the temperature to 630 ° C, the plate upper surface temperature, from the plate upper surface to 1/4 plate inside, that is, 1/4 plate upper surface The temperature rise curves for the temperature, the center temperature of the plate thickness and the average temperature are shown. Five inductors were required to achieve the temperature rise of 630 ° C. Moreover, after lowering the surface temperature between the inductors, intermittent heating was performed by heating with the next inductor.

(Example 2) In the example of the present invention, the plate thickness 5 is shown in FIG.
About 0 mm thick steel plate, using the inductor of the above specifications, when heating from 20 ° C to 650 ° C and raising the temperature to 630 ° C, the plate upper surface temperature, from the plate upper surface 1/4 plate inside, that is, 1/4 plate upper surface The temperature rise curves for the temperature, the center temperature of the plate thickness and the average temperature are shown. Eight inductors were required to achieve the temperature rise of 630 ° C. Moreover, after lowering the surface temperature between the inductors, intermittent heating was performed by heating with the next inductor.

[0054]

EFFECT OF THE INVENTION As compared with the conventional gas-fired furnace, highly efficient heat treatment equipment can be provided at a lower cost. From thin to thick materials, it is possible to realize highly accurate uniform heating of ± 10 ° C in the plate thickness / plate width direction at the end of heating. It can be heated without causing deformation, warpage and meandering due to heating strain of the material.

[Brief description of drawings]

[Fig. 1] F when heating is started from about 20 ° C near room temperature
Explanatory diagram showing the relationship between (a coefficient indicating the degree of occurrence of a temperature difference) and χ (χ = t / δ, the relationship between the plate thickness t and the penetration depth δ).

FIG. 2 shows χ (χ = t / δ, the relation between the plate thickness t and the penetration depth δ) and Q under the condition of a flat plate (width direction infinity condition).
Explanatory diagram showing the relationship of (power absorption coefficient)

[Fig. 3] Comparison of required soaking time according to plate thickness of thick steel plates and passage time between induction heating devices for thick steel plates when heated at the same efficiency

[Fig. 4] Maximum temperature rise per inductor is about 40
Temperature rising characteristic graph showing an example of heating a thick steel plate (plate thickness 20 mm) at 0 ° C.

FIG. 5 is a temperature rise characteristic graph showing an example of heating a thick steel plate (plate thickness 12 mm) in an example of the method of the present invention.

FIG. 6 is a temperature rise characteristic graph showing an example of heating a thick steel plate (plate thickness 50 mm) in an example of the method of the present invention.

   ─────────────────────────────────────────────────── ─── Continued front page    (72) Inventor Akane Tagane             1-2-1, Marunouchi, Chiyoda-ku, Tokyo             Main Steel Pipe Co., Ltd. (72) Inventor Akio Fujibayashi             1-2-1, Marunouchi, Chiyoda-ku, Tokyo             Main Steel Pipe Co., Ltd. (72) Inventor Atsushi Watanabe             1-2-1, Marunouchi, Chiyoda-ku, Tokyo             Main Steel Pipe Co., Ltd. F term (reference) 3K059 AA09 AB25 AB28 AC12 AC33                       AC37 AD05 AD34 CD65 CD72                       CD75

Claims (7)

[Claims] 1. In a heat treatment apparatus for a thick steel plate in which a plurality of solenoid type induction heating devices (hereinafter referred to as inductors) are arranged in series, a steel plate surface temperature does not exceed a target upper limit temperature below a magnetic transformation point (Curie temperature). In addition, a heat treatment apparatus for thick steel plates, characterized in that a single unit temperature rise amount of each inductor is set. 2. The heat treatment apparatus for a thick steel plate according to claim 1, wherein the surface temperature is lowered between the inductors, and then intermittent heating is performed by heating with the next inductor. 3. The thick steel sheet according to claim 1 or 2, characterized in that the distribution of the input power of each inductor is changed so that the average temperature of the thick steel sheet on the output side of each inductor satisfies the target value. Heat treatment equipment. 4. The heating frequency of each inductor is set to 200H.
The heat treatment apparatus for a thick steel plate according to any one of claims 1 to 3, wherein the heat treatment device has a frequency of z to 2000 Hz. 5. The single unit temperature rise of each inductor is 400 ° C.
The heat treatment apparatus for a thick steel plate according to any one of claims 1 to 4, wherein three or more inductors are arranged in series below. 6. The coil length of each inductor is 1.5 m
The heat treatment apparatus for a thick steel plate according to any one of claims 1 to 5, wherein: 7. The heat treatment apparatus for a thick steel plate according to claim 1, wherein the inductors are arranged at a distance of 300 mm or more.