WO2011081387A2

WO2011081387A2 - Sheet-material forming device and method

Info

Publication number: WO2011081387A2
Application number: PCT/KR2010/009383
Authority: WO
Inventors: 강범수; 구태완; 허성찬; 서영호
Original assignee: 부산대학교 산학협력단
Priority date: 2009-12-28
Filing date: 2010-12-28
Publication date: 2011-07-07
Also published as: KR101166171B1; KR20110075724A; US20120291512A1; WO2011081387A3

Abstract

Disclosed are a sheet-material forming device and method in which the response to modifications and changes in a target shape is flexible and in which a conventional forming punch block can be used in order to form even curved surfaces comprising localised small radiuses of curvature or edges. The sheet-material forming device of the present invention is equipped with a top and bottom variable mould between which a sheet material to be formed is placed, and which can move upwards and downwards and comprises a combination of a plurality of mould blocks for forming curved surfaces comprising different radiuses of curvature and localised small radiuses of curvature and/or edges; and the plurality of mould blocks comprise forming punch blocks having an array of forming punches for forming curved-surface parts having a predetermined radius of curvature, and comprise integral mould blocks having forming parts for forming curved-surface parts comprising localised small radiuses of curvature and/or edges. The forming punch blocks comprise 1st, 2nd, 3rd ... Nth forming punch blocks having an array of forming punches of differently sized cross-sectional areas, while the integral mould blocks comprise edge-forming blocks for forming curved-surface parts comprising edges, and also comprise small-radius-of-curvature-forming blocks for forming curved-surface parts comprising local small radiuses of curvature. The mould blocks respectively comprise supporting members for supporting the forming punches or the forming parts and also for joining to neighbouring mould blocks.

Description

Sheet metal forming apparatus and method

The present invention relates to a device and a method for manufacturing a plate molded article, such as shipbuilding shell, railcar shell, aircraft exterior, automotive exterior, and the like, in particular a plate-shaped product having multiple curvatures, local curvature and / or edges It relates to a sheet forming apparatus and method for molding using a conventional forming punch block.

In general, a molding apparatus and method using a mold have been widely used in molding a plate-shaped product having a multi-curvature and a curved surface including local curvature or edges. The sheet metal forming apparatus and method using such a metal mold | die are widely used especially for the process of the board | plate material for exterior structures of a vehicle.

A general sheet metal forming apparatus and method are to form a plate-shaped product having a target shape by combining upper and lower molds having a molded portion of a target shape with a press device.

However, the general sheet forming apparatus and method as described above is effective for mass production of a single product, because the sheet can be formed only in the shape provided in the upper and lower molds, but a new mold reflecting this when the target shape is modified or changed. Because it must be manufactured, due to the increase in the mold processing cost, etc., it is not suitable for small quantity production of many kinds.

In particular, in the case of the plate-shaped product for the exterior structure of the vehicle, the target shape is modified or deformed several times in the initial design stage. In forming such a plate-shaped product for the exterior structure of the vehicle, a general sheet forming apparatus and method are described. It is not suitable in terms of cost and time because it is necessary to change the object shape of the mold every time the shape and structure change.

In order to solve this problem, US Pat. No. 4,212,188, Japanese Patent Application No. 46-37088, etc., a multi-point variable press-type sheet metal forming apparatus comprising a plurality of punches each of which the upper mold and the lower mold are individually movable up and down. It is starting. Such a multi-point variable press-type sheet metal forming apparatus can flexibly cope with a simple method of appropriately adjusting the height of punches of upper and lower molds when the target shape is modified or deformed.

However, the above-described general multi-point variable press-type sheet metal forming apparatus is effective for forming a smooth curved surface as described above, but there is a problem that a curved surface having a locally small curvature radius or a curved surface having corners is difficult to form.

SUMMARY OF THE INVENTION The present invention has been made in view of the above-described aspects, and it is flexible to cope with modification and deformation of a target shape, and a sheet forming apparatus and method suitable for forming a prototype in an initial design stage of a multi-product small quantity product or a vehicle exterior structure. The purpose is to provide.

Another object of the present invention is to provide an apparatus and method for forming a sheet material which can form a curved surface having a locally small curvature radius and / or an edge using an existing molding punch block.

Plate forming apparatus according to the present invention for achieving the above object is a plurality of for forming a curved surface which can be moved up and down with a molded plate between, and comprising different curvature radius and locally small curvature radius and / or corners. The upper and lower variable molds which combine the metal mold blocks of this invention are provided. The plurality of mold blocks may include molding punch blocks having a plurality of molding punches arranged to form curved portions having a predetermined radius of curvature; And integral mold blocks having molding portions for forming curved portions including locally small curvature radii and / or edges.

According to a preferred embodiment, the forming punch blocks may include first, second, third, ..., N-th forming punch blocks in which forming punches having cross-sectional areas of different sizes are arranged. The molding punch block may include a support member for supporting the molding punches and joining the neighboring mold blocks.

In addition, the forming punches of the forming punch blocks may be configured to enable individual height adjustment, the forming punch may also be formed in a circular or polygonal cross-sectional shape, the end may be curved.

In addition, an elastic pad for forming a smooth curved surface may be interposed between the upper and lower molds of the variable mold and the formed plate member.

According to a preferred embodiment, the unitary mold blocks may include an edge forming block for forming a curved portion including an edge, and a small curvature radius forming block for forming a curved portion including a local small radius of curvature. Each of the corner forming block and the small radius curvature block may include a supporting member for supporting a molding unit and for coupling with a neighboring mold block.

In addition, the sheet metal forming apparatus according to the present invention, the fixing die for fixing a plurality of mold blocks selected and combined according to the target shape of the formed plate material; And a molding punch height control module configured to adjust the heights of the molding punches so that the molding punches of the mold block combined form a molding surface of the mold according to a desired shape.

On the other hand, the plate forming method for achieving the object of the present invention, the step of modeling the target shape to be molded on the plate; Selecting and combining mold blocks corresponding to the curvature and the curved shape according to the modeling of the step, and adjusting the height of the forming punches to form a molding surface for the desired shape; Correcting the forming surface; And final molding the plate.

The shaping surface correction step may include forming a prototype; Measuring the shape of the prototype to determine whether it is within an error range; And reconstructing the molding surface when the measured value of the prototype does not satisfy the error range.

Alternatively, the shaping surface correction step may include analyzing the configured shaping surface; Predicting the elastic recovery amount of the sheet through the elastic recovery analysis; Predicting and measuring the shape of the prototype from the above analysis result to determine whether it is within an error range; And reconstructing the molding surface when the measured value of the predicted prototype does not satisfy the error range.

In the sheet forming method according to the present invention, in any case, the forming surface reconstruction step may be repeated until the prototype or the predicted prototype measurement results satisfy the error range.

According to the present invention as described above, by forming a variable mold by selecting a forming punch block and an integral mold block (edge molding block or small curvature radius forming block) corresponding to the curvature and curved surface according to the modeling of the target shape, Modifications and modifications are flexible, and in particular, a curved surface having a local small radius of curvature or corner, which is difficult to be formed by a general molding punch block, can be formed by combining the molding punch block with only the integrated mold block.

Therefore, it is not necessary to manufacture a completely new mold for each variety when forming a multi-product small quantity product, thereby reducing costs and improving productivity. In addition, in the initial prototype design of a vehicle where frequent modifications and changes of the target shape are required, existing punch punch blocks may be manufactured by manufacturing only one-piece mold blocks having a local radius of curvature or corners without having to manufacture a new mold every time the shape of the exterior material is changed. It can be configured in conjunction with the variable mold, which can reduce the cost and development period.

In addition, the sheet forming apparatus and method according to the present invention can constitute a variable mold corresponding to any desired shape, regardless of the type and thickness of the material, and is composed of different materials, materials having different thicknesses, isotropy and anisotropy. It can be advantageously used in terms of cost and time for forming a single curvature, a double curvature, a multicurvature, and a curved surface having a local small curvature radius or corner.

1 and 2 are a perspective view showing an example of the forming punch block constituting a variable mold of the sheet metal forming apparatus according to the present invention,

3 is a perspective view of an edge forming block which is an example of an integrated mold block constituting a variable mold of a sheet metal forming apparatus according to the present invention;

Figure 4 is a perspective view of a small curvature radius forming block which is another example of an integrated mold block constituting a variable mold of the sheet metal forming apparatus according to the present invention,

5 is a cross-sectional view showing an example of configuring a variable mold using the mold blocks shown in Figures 1 to 4;

6 is a cross-sectional view showing an example of forming a plate using the variable mold of FIG.

7 is a cross-sectional view showing another example of configuring a variable mold using the blocks shown in FIGS. 1 to 4;

8 is a cross-sectional view showing an example of forming a plate using the variable mold of FIG.

9 is a perspective view showing an example of three-dimensional modeling of the desired shape;

10A and 10B are a plan view and a sectional view of a variable mold configured to correspond to the target shape of FIG. 9;

11 is an exploded perspective view showing an arrangement example of a variable mold, a fixed die, and a forming punch height control module configured for forming a molded curved surface including both a corner portion and a curved portion having a local small radius of curvature;

12 is an assembly view of FIG. 11, and

13 is a process chart of a sheet forming method using a sheet forming apparatus according to the present invention.

Molding

Punch Blocks

11,11 ', 21 Molding Punch

30,30 '; Curved Molding Block 40,40'; Bending Curvature Radius Block

12,12 ', 22,32,32', 42,42 '; support member

50; elastic pad 100; bottom deformation type

200; upper side deformation type 300; fixed die

400; forming punch height control module

BEST MODE Hereinafter, preferred embodiments of the present invention will be described in detail with reference to the accompanying drawings. For reference, in describing the embodiments of the present invention, if it is determined that a detailed description of a related known function or configuration may unnecessarily obscure the subject matter of the present invention, a detailed description thereof will be omitted.

1 to 4 illustrate the mold blocks constituting the variable mold of the sheet metal forming apparatus according to an embodiment of the present invention, Figures 1 and 2 is an embodiment of the forming punch blocks, Figures 3 and 4 are integral molds Are perspective views schematically illustrating an embodiment of the blocks.

As shown in FIGS. 1 and 2, the forming

punch blocks

10 and 20 may include a plurality of forming

punches

11 and 21 arranged in a matrix, and a supporting member 12 for supporting the forming

punches

11 and 21. 22).

The forming

punches

11 and 21 have different diameters. The forming punch block 20 having the forming punch 21 having a relatively large diameter is for forming a relatively smooth curved portion, and the forming punch block 10 having the forming punch 11 having a smaller diameter is smaller than the curved portion. It is for shaping a sharp curved portion.

On the other hand, although not shown, the sheet forming apparatus according to the present invention, in addition to the blocks having a molding punch having a diameter as shown, a plurality of forming punch blocks having a plurality of forming punches having a diameter of a variety of sizes (10, 20, ..., N). Using such a plurality of forming punch blocks (10, 20, ..., N) it is possible to form a curved surface having a variety of curvature radius.

In addition, although the shape of the forming

punches

11 and 21 is circular in FIGS. 1 and 2, the forming

punches

11 and 21 are not necessarily formed in a circle, but may be formed in a polygon such as a triangle or a rectangle. Can be. In addition, end portions of the forming

punches

11 and 21 are rounded, as shown in FIGS. 5 to 8.

The

support members

12 and 22 accommodate and support the corresponding forming

punches

11 and 21. The molding punches 11 and 21 are individually adjustable in height while being supported by the

support members

12 and 22. Individual height adjustment of the molding punches 11 and 21 is performed by the molding punch height adjusting module 400 shown in FIGS. 11 and 12. In addition, the

support members

12 and 22 are not specifically illustrated in the drawings, but have fastening structures for coupling with neighboring mold blocks. Since this fastening structure is a normal fastening structure detachable from each other, detailed description thereof will be omitted here.

As shown in Figs. 3 and 4, the integrated mold blocks 30 and 40 have

molding parts

31 and 41 and supporting

members

32 and 42 for supporting the

molding parts

31 and 41.

The molded part 31 of the integrated mold block 30 shown in FIG. 3 is for molding an edge, and the molded part 41 of the integrated mold block 40 shown in FIG. 4 has a curved surface having a local small curvature radius. It is for molding a part. In addition, although not shown, the

support members

32 and 42 are provided with fastening structures for coupling with neighboring mold blocks. Since the fastening structure is also a conventional fastening structure detachable from each other, a detailed description thereof will be omitted.

3 and 4 illustrate only one shape of the corner shaped portion 31 and the small radius of curvature forming portion 41, the plate forming apparatus according to the present invention has a plurality of integral mold blocks having various shapes of the forming portion ( 30, 40, ..., N).

1 to 4 as described above, by appropriately selecting and combining a plurality of mold blocks according to the target shape, it is possible to form an upper and lower variable mold having a molding surface corresponding to any desired shape. For example, when a variety of varieties are produced in a small quantity production process, or when the shape of the exterior material is modified or changed in the design stage of the vehicle, a plurality of molding punch blocks 10, 20, It is possible to directly reconfigure the variable mold having the desired molding surface by selecting the corresponding one from ..., N) or the integrated mold blocks 30, 40, ..., N. Therefore, it is possible to reduce the cost and time waste of newly manufacturing the entire mold.

On the other hand, the corner forming block or the bending modulus of the radius of curvature blocks can not know how the shape of the exterior material is changed in the design stage of the vehicle, etc., it can not be made in advance for the number of all cases. However, it is possible to reconstruct the variable mold by manufacturing only the forming block corresponding to the curved edge of the changed corner portion or the small radius of curvature and combining with the existing forming punch blocks. In other words, when the target shape is modified or changed, it is much more advantageous in terms of cost and time to manufacture only the mold block corresponding to the changed part as described above, rather than newly manufacturing the entire mold.

5 to 8 illustrate an example of configuring a variable mold having a molding surface corresponding to a target shape by using a plurality of mold blocks as described above, and FIGS. 5 and 6 include curved surfaces having edges. 7 and 8 are exemplary views illustrating the configuration of a variable mold in the case of including a curved portion having a local small radius of curvature.

The lower deformable mold 100 for forming an object-shaped product including a curved portion having an edge is formed by forming forming punches 21 having a relatively large diameter to form a smooth curved portion, as shown in FIG. 5. The block 20 is disposed at the center portion, and two corner forming blocks 30 and 30 'having molding portions 31 and 31' for forming curved surfaces having corners on both sides of the forming punch block 20 are formed. The forming punch blocks 10 and 10 ′ are arranged on both sides of the forming punch blocks 10 and 10 ′, in which forming punches 11 having a smaller diameter are arranged to form curved portions that are sharper than the curved portions.

Each of the mold blocks 10, 30, 20, 30 ', and 10' disposed as described above is coupled to each other by the supporting

members

12, 32, 22, 32 ', and 12' of each mold block. The forming punches 11, 21, 11 ′ of the forming punch blocks 10, 20, and 10 ′ have their heights adjusted to the heights calculated according to the curvature radii of the target shapes. In addition, the upper portion of the forming punch (11, 21, 11 ') is provided with an elastic pad 50 for forming a smooth curved surface as a whole.

In FIG. 6, 200 is an upper deformable mold, and P is a formed plate material. The upper variable mold 200 is configured in the same manner as the lower variable mold 100 as described above. However, the molding surface profile of the upper deformable mold 200 is configured to have a shape opposite to the molding surface profile of the lower deformable mold 100 so as to form a plate using the upper and lower

variable molds

200 and 100.

The upper and lower

variable molds

200 and 100 configured as described above are connected to, for example, a press device (not shown), and the upper and lower

variable molds

200 and 100 are positioned between the upper and lower

variable molds

200 and 100, and then the upper and lower

variable molds

200 and 100 are driven. By approaching the

molds

200 and 100, the plate is molded into a desired target shape. At this time, between the forming punches (11a, 21a, 11 'a) of the upper deformable mold 200 and the molded plate (P) is interposed between the elastic pad (50') to form a smooth curved surface as a whole.

7 and 8 reconstruct the upper and lower variable molds when the object shape of the plate to be molded is partially changed, that is, when the object shape of FIGS. 5 and 6 is changed into a curved surface having a local small curvature radius instead of a curved surface having corners. It shows an example of molding.

In this case, the corner forming blocks 30 and 30 'are removed and the small bending radius forming blocks 40 and 40' are inserted in place to form new upper and lower variable molds 200 'and 100'. The configuration other than the use of the bending modulus radius shaping blocks 40 and 40 'instead of the corner shaping blocks 30 and 30' is the same as the case of FIGS. 5 and 6 described above, and thus the same or related reference numerals are used herein. Detailed description will be omitted.

When the target shape is modified and changed as described above, by changing only the mold block corresponding to the changed part, a variable mold having a molding surface corresponding to the modified target shape can be inexpensively and quickly reconfigured to form a product. In this case, even if there is no pre-precision radius curvature block, only the small radius curvature block is newly manufactured and combined with an existing molding punch block to form a variable mold. Compared to this, the cost and time can be greatly reduced.

On the other hand, when the curvature of the curved surface portion of the target shape is changed, the molding surface corresponding to the target shape can be easily and quickly configured by a simple method of adjusting the height of the molding punch of the molding punch blocks.

Figure 9 shows an embodiment of the three-dimensional modeling of the target shape to be formed on the plate. According to this example, the objective shape is a smooth curved portion 5-1, a curved portion 5-2 (5-3) and a corner curved portion 5-4 (5) that are sharper than the curved portion 5-1. It is a shape having -5).

10A and 10B illustrate a plan view and a cross-sectional view of the lower deformable mold 100 configured by combining the selected mold blocks according to the above-described three-dimensional modeling of the target shape and adjusting the height of the forming punches in response to the curvature of the curved portion. .

As shown in Figs. 10A and 10B, a molding punch block 20 in which molding punches having a relatively large diameter are arranged is disposed at a smooth curved portion 5-1 of the target shape, and the curved portion 5 is formed. In the position of curved portions 5-2 and 5-3 which are relatively sharper than 1), forming punch blocks 10 and 10 'are formed in which forming punches having a relatively small diameter are arranged, and corner curved portions 5- 4) (5-5), corner forming blocks 30 and 30 'are arranged to form a variable mold 100. Here, the forming punches are adjusted to a height calculated according to the radius of curvature of the curved portion. In addition, the elastic punch 50 is installed in the molding punch is adjusted height.

11 is an exploded perspective view showing an example of arrangement of a variable mold for forming a molded surface including both a corner and a local curvature radius, a fixed die for fixing the variable mold, and a molding punch height control module; 12 is an assembly view of FIG.

As shown in Figures 11 and 12, the variable mold 100 is formed of a molded punch block (10, 10 ') consisting of forming punches (11, 11') and a curved surface having an edge for forming any formed curved surface The edge forming block 30 for forming and the small curvature radius forming block 40 for forming a curved surface having a locally small curvature radius are configured by fastening each other.

Variable mold 100 fastened as described above is fixed or inserted into the fixed die 300. The fixing die 300 serves to fix the variable mold composed of a combination of a plurality of mold blocks, and also to support the upper variable mold (not shown).

A molding punch height control module 400 is disposed below the fixed die 300. The molding punch height control module 400 is to adjust the height by moving each forming punch up and down individually, it may be configured to include a number of punch control motor corresponding to each forming punch. In addition, the molding punch height control module 400 may be configured to adjust the height of the molding punch while moving one or three to four punch control motor in the row and column direction.

According to a preferred embodiment, the molding punch height control module 400 adjusts the height of the plurality of forming punches to receive the curved surface data of the target shape to form the curved surface, the drive control of the punch control motor To adjust the height of the forming punches.

Hereinafter, a method of molding a plate using the plate forming apparatus as described above with reference to FIG. 13 will be described.

First, the target shape is three-dimensional modeled (S510). According to the modeling, the mold block according to the curvature and the curved shape of the target shape is selected and combined, and the forming surface of the target shape is configured by adjusting the height of the forming punches (S520). Then, the correction process for the primary molding surface as described above is performed (S530).

The forming surface correction process (S530) is performed by selecting one of a test-based method and an analysis-based method (S531). In the molding surface correction method based on the test, first, the prototype is molded by using a variable mold having a primary molding surface as described above (S532). Thereafter, the shape of the prototype obtained by the molding of step S532 is measured (S533), and it is determined whether the measured value is in the error range (S534).

If the shape measurement value of the prototype in the step S534 satisfies the error range, the plate is molded (S540). However, if the shape measurement value of the prototype in step S534 does not satisfy the error range, the step of reconstructing the molding surface is performed (S535).

Here, the step of reconstructing the molding surface refers to a series of operations such as re-adjusting the height of the forming punches or replacing the integral mold block so that the shape measurement value of the prototype satisfies the error range.

After reconstructing the molding surface in the secondary as described above, the prototype is again molded with the corrected molding surface, and the shape of the prototype is measured, and it is determined whether the measured value is in the error range. If it is in the error range, the molding is performed, and if the error range is not satisfied, the above process is repeated.

In the shaping plane correction method based on the analysis, first, a shaping analysis using a computer or the like is performed on the shaping plane configured first (S536). Then, the elastic recovery analysis of the plate is performed using the finite element method (S537), and the shape of the prototype is predicted and measured from the final result (S538). If the error range is satisfied from the measurement result, the plate is molded (S540). If the error range is not satisfied, the molding surface is reconstituted (S535).

After reconstructing the molding surface as secondary, measure the predicted prototype obtained by performing the molding analysis and the elastic recovery analysis of the corrected molding surface, and determine whether the measured value satisfies the error range. If the step is not satisfied, the molding surface reconstruction step is performed, and this series of steps is repeated until the measured value of the predictive prototype satisfies the error range.

As described above, in the sheet forming method according to the present invention, after forming a molding surface of the mold by combining a plurality of mold blocks, the molding surface is corrected in real time by a test-based method or an analysis-based method. Since molding is performed after that, defects can be reduced.

In the above, the present invention has been described by way of example. The terminology used herein is for the purpose of description and should not be regarded as limiting. Many modifications and variations of the present invention are possible in light of the above teachings. Accordingly, the invention may be freely practiced within the scope of the claims unless otherwise stated.

Claims

Plate molding having upper and lower variable molds formed by combining a plurality of mold blocks capable of moving up and down with a plate to be formed therebetween and forming a curved surface including different curvature radii and locally small curvature radii and / or edges. As a device,

The plurality of mold blocks,

Forming punch blocks having a plurality of forming punches arranged to form curved portions having a predetermined radius of curvature; And

Plate forming apparatus comprising a; one-piece mold blocks having a molded part for forming a curved portion comprising a locally small curvature radius and / or corners.
The method of claim 1,

The forming punch blocks may include first, second, third, ..., N-th forming punch blocks in which forming punches having cross-sectional areas of different sizes are arranged.

Each of the forming punch block comprises a support member for supporting the forming punch and the coupling with the neighboring mold block.
The method of claim 2,

Forming punches of the forming punch blocks are plate forming apparatus, characterized in that the individual height adjustment is possible.
The method of claim 2,

The forming punch is a plate forming apparatus, characterized in that the cross-sectional shape is circular, the end is curved.
The method of claim 2,

The forming punch is a cross-sectional shape of a polygonal plate, characterized in that the end portion is curved sheet forming apparatus.
The method of claim 2,

Plate forming apparatus, characterized in that it comprises an elastic pad for forming a smooth curved surface interposed between the upper and lower variable mold forming punches and the formed plate material.
The method of claim 2,

The one-piece mold block, an edge forming block for forming a curved surface portion including a corner; And a small curvature radius forming block for forming a curved portion including a local small radius of curvature.

The corner forming block and the small bending radius radiused block, each of the plate forming apparatus, characterized in that it supports a molding portion and has a support member for coupling with a neighboring mold block.
The method of claim 7, wherein

A fixing die for fixing a plurality of mold blocks selected and combined according to a desired shape of a plate to be formed; And

And a forming punch height control module for adjusting the heights of the forming punches so that the forming punches of the mold block form a forming surface according to a desired shape.
A plate forming method using a plate forming apparatus according to any one of claims 1 to 8,

a) modeling a desired shape to be molded into the sheet;

b) selecting and combining the mold blocks corresponding to the curvature and the curved shape according to the modeling of the step, and adjusting the height of the forming punches to form a molding surface for the desired shape;

c) correcting the forming surface; And

d) forming the plate material; final forming method.
The method of claim 9, wherein c) is

Molding the prototype;

Measuring the shape of the prototype to determine whether it is within an error range; And

And reconstructing the forming surface when the measured value of the prototype does not satisfy the error range.
The method of claim 9, wherein c) is

Analyzing the configured molding surface;

Predicting the elastic recovery amount of the sheet through the elastic recovery analysis;

Predicting and measuring the shape of the prototype from the above analysis result to determine whether it is within an error range; And

And reconstructing the molding surface when the measured value of the predicted prototype does not satisfy the error range.
The method according to claim 10 or 11, wherein

The forming surface reconstituting step is a plate forming method, characterized in that to perform repeatedly until the prototype satisfies the error range.