JP2002048121A - Bolt and manufacturing method thereof - Google Patents

Abstract

PROBLEM TO BE SOLVED: To provide a bolt which has an aligning function to rectify so as to be coaxial upon engagement with a nut even when the axis line is in inclination and in which dents and the like can hardly occur to a screw thread face. SOLUTION: An integral continuation part of guide having a radius corner part of which radius is reduced gradually in arc-shaped cross section from the outer diameter roughly equal to a screw effective diameter or a major diameter is formed at the tip potion of the bolt, and the screw thread is designed in such manner that the screw end terminates at the middle of the radius corner part of the integral continuation part of guide. The end surface which coincides with a terminus of the radius corner part can be a flat plane approximately perpendicular to the screw axis or can be a predetermined curved surface. When an amount of extension of the integral continuation part in screw shaft direction is denoted by L, and a radius of curvature of the radius corner part is denoted r, then L/r is, for instance, selected as 0.65 to 1.5, and when a pitch of a male screw is indicated as P and the radius of curvature is indicated as r, then r is set within the range of P to 3P, or 1.5P to 2.5P.

Description

DETAILED DESCRIPTION OF THE INVENTION

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to a bolt and a method for manufacturing the bolt.

[0002]

2. Description of the Related Art Conventionally, in a general bolt, a thread end which is an incomplete thread portion of a male thread portion tends to have a thin and thin cross section. May occur. Further, since the strength of the screw end is not necessarily high, there is a disadvantage that dents are easily formed.

A conventional bolt with a guide projection is known which is inserted into a female screw hole of a nut to be screwed and coaxially aligns both axes prior to screwing of the bolt and the nut. ing. However, since the guide protrusion enters the female screw hole of the nut with a predetermined gap, only a very rough guide function can be expected. In addition, the protruding guide projections increase the weight and reduce the material yield.

[0004]

SUMMARY OF THE INVENTION The present invention relates to a bolt and a method of manufacturing the same, which perform a high-precision axis alignment function when screwed with a female screw member such as a nut and hardly cause dents or the like at the screw ends. Is to provide.

[0005]

Means for Solving the Problems and Effects of the Invention The bolt according to the present invention has a rounded corner portion at the tip end of the bolt which gradually reduces in diameter in an arc shape in cross section from an outer diameter substantially equal to the effective screw diameter or the outer diameter of the screw. A guide extension is formed, and a screw thread is formed so that a screw end comes in the middle of a round corner portion of the guide extension.

[0006] Further, such a method of manufacturing a bolt is characterized in that a rounded corner portion is provided at the tip end of the bolt intermediate member before forming the screw, the diameter of which gradually decreases in an arc-shaped cross section from an outer diameter substantially equal to the effective screw diameter or the outer diameter of the screw. Is formed in advance, and a thread is formed by leaving a round corner portion partially such that a screw end comes to the middle of the round corner portion of the guide extension portion.

[0007] When such a round corner portion remains at the tip of the bolt, when the screw is engaged with a female screw member such as a nut, the round corner portion comes into contact with a female screw opening end of a mating nut or the like, so to speak. Even when the nuts are swung like a spherical joint and the axes of the nut and the bolt are inclined, an action of coaxially correcting the inclination can be generated.

Further, since the screw end starts (or ends) from the middle of the rounded corner portion, the thin screw end having low strength, and furthermore, "falling" of the screw end hardly occurs, which is advantageous in terms of the strength of the screw end. The strength against marks and the like is also large, and the reliability is improved.

[0009] Here, the front end surface substantially coincident with the end of the rounded corner portion of the guide extension portion can be a flat surface substantially perpendicular to the screw axis, thereby minimizing the protrusion of the guide extension portion and reducing the material. Good yield and light weight. However, the end of the radius corner is a flat surface,
The central portion may have a concave shape, or may be formed along a predetermined concave curved surface, a convex curved surface, or the like.

When the amount of protrusion of the guide extension in the screw axis direction is L, the radius of curvature of the rounded corner is r, and the pitch of the male screw of the bolt is P, L / r is 0.65 to 0.65.
It can be said that 1.5 and r are desirably set in the range of P to 3P or 1.5P to 2.5P from the viewpoint of the above-described centering function and impact resistance.

Further, when the present invention is considered limited to a rolled bolt, a round corner which gradually reduces in diameter from the outer diameter substantially equal to the effective diameter of the screw to an arc-shaped cross section is provided at the tip of the bolt intermediate member before thread rolling. A guide extension having a portion is formed in advance by forging with a bolt body portion, and a thread is formed by partially leaving a radius corner so that a screw end comes in the middle of a radius corner of the guide extension. The manufacturing method of rolling can be adopted.

Further, when the present invention is considered limited to a cutting screw, a round corner portion which gradually reduces in diameter from the outer diameter substantially equal to the outer diameter of the screw to an arc-shaped cross section is provided at the tip of the bolt intermediate member before the screw is cut. A guide extension having a bolt body is formed in advance by forging together with a bolt body, and a thread is cut while leaving a radius corner part partially in the middle of the radius corner of the guide extension. The adoption of a manufacturing method is also possible.

[0013]

Embodiments of the present invention will be described below with reference to embodiments shown in the drawings. In the embodiment shown in FIG. 1, a round corner portion 6 is formed at the distal end portion of the bolt 1, and the distal end of the round corner portion 6 is configured as a flat surface 5. That is, the bolt 1 in FIG. 1 includes a bolt head 2 and a leg (bolt shaft) 3, and a guide extension portion (a guide projection-shaped portion) having a round corner portion 6 is provided on the outer peripheral edge of the distal end portion of the bolt shaft portion 3. 7) is formed.

The screw end 8a of the male screw portion 8 is located in the middle of the round corner portion 6. In other words, the male screw portion 8 starts (or can be said to end) from the middle of the round corner portion 6 and follows the round corner portion 6. Thus, a flat surface 5 substantially perpendicular to the bolt axis is formed. The end of the rounded corner 6 does not necessarily have to be a flat surface as described above, but may be, for example, a concavely concave surface or a convexly swelled surface.

As shown in FIG. 2, the radius corner portion 6 is formed of a part of a substantially spherical surface or a part of a curved surface approximating the spherical surface, and has a radius of curvature of rc. One end of the round corner portion 6 is formed such that an arc cross section or an arc cross section curve defining the corner portion 6 substantially contacts the effective screw diameter db of the male screw portion 8, and the other end of the round corner portion 6 is formed. In this example, the end is formed such that its circular section or circular section curve substantially contacts the flat surface 5. The length (projection amount) of the extension portion (guide extension portion) 7 including the rounded corner portion 6 in the bolt axis direction is L, and the end portion of the shaft portion centering on the bolt center line O (flat surface) ) 5 is φ.

As will be described later, in a bolt intermediate product before forming a male screw, the bolt shaft portion and the round corner portion 6 before forming the male screw are smoothly continuous, and in a cross section including the bolt axis, the round corner portion 6 and the round corner portion are not formed. Are connected in a tangential manner to the bolt shaft portion. Then, as shown conceptually in FIG. 3, when a male screw is rolled (rolled screw), the flesh of a portion that becomes a thread root moves to form a thread and a male screw is formed (thread rolling). (The lower diameter is the shaft diameter of the bolt intermediate product before the screw is formed.) Therefore, the end of the round corner portion 6 is formed with the effective screw diameter db as a starting point or an end point, and comes between the screw inner diameter dc and the screw outer diameter da. It will be.

On the other hand, as shown in FIG. 4, when a male screw of a bolt is formed by cutting (cutting screw), a portion corresponding to a thread root is removed by cutting to form a screw thread (thread cutting lower diameter). Is the shaft diameter of the bolt intermediate product before thread formation), so that the end of the round corner portion 6 is formed with the screw outer diameter da as a starting point or an end point. However, in the following, it will be represented by an example of a rolled screw.

As described above, since the outer peripheral portion of the extension portion 7 is the round corner portion 6, the round corner portion 6 is formed.
When a screw is engaged with a mating female screw member such as a nut, a function of guiding the two screw members such as the bolt and the nut so that their axes are aligned with each other is exerted. FIG. 5 conceptually illustrates this, and it is assumed that the axis O2 of the nut 10 is inclined at an angle θ with respect to the axis O1 of the bolt 1 when the above-described bolt 1 and nut 10 are screwed together. . In general, the two axes of the bolt and nut are not ideally coaxial at the time of screwing, and the axes are more or less inclined relative to each other.

When the bolt / nut is pressed in the inclined state (or one of them is rotated while pressing), the nut 10 is moved along the spherical round corner 6 formed at the tip of the bolt 1. The opening end of the nut slides (slids), and the axis O2 of the nut 10 relatively rotates in a direction coaxial with the axis O1 of the bolt 1, and
It acts to correct the inclination of both axes of the nut. As a result, even if there is some inclination of the axis,
The nut can start screwing satisfactorily, and it is possible to prevent or reduce biting (biting) and seizing due to the inclination of the axis.

As shown in FIG. 12, in the conventional general bolt 101 having no rounded corner, the screw end 108a, which is an incompletely threaded portion of the male threaded portion 108, tends to have a thin and thin cross section. As a result, a “fall” may occur in which the screw end is deformed so as to deviate from the normal spiral. On the other hand, the above-mentioned radius corner 6 (R)
In the bolt 1 in which the radius is formed, the outer diameter is gradually reduced spherically by the radius corner portion 6 to reach the shaft end face 5, and the screw end 8a starts (or ends) from the middle of the radius corner portion 6, so that the strength is reduced. Low-profile thin screw ends, and thus "falling" of the screw ends are less likely to occur, which is advantageous in terms of the strength of the screw ends,
The strength against dents that are likely to occur during transportation and processing drops is large, and reliability is improved.

In the related art, as shown in FIG. 13, there is a bolt 111 provided with a nut hole insertion projection 112 protruding in a spherical shape with a two-stage shaft at the tip of the bolt. The outer diameter de of the protrusion 112 is much smaller than the diameter (thread effective diameter db) and smaller than the screw inner diameter dc. After the thread is rolled, there is a gap between the screw inner diameter dc and the protrusion diameter de. G occurs. That is,
Since the screw end 118a of the male screw portion 118 is not formed in the middle of the protrusion 112, there is no effect of preventing the above-mentioned fall. Further, the protrusion 112 makes the axes of the bolts and nuts close to each other within a certain distance range (constraining the coaxiality of the bolts and nuts under a certain range of conditions) so that the screwing can be smoothly performed. It is not intended to correct even a certain range of coaxial misalignment. Therefore, the larger the allowable range of the misalignment, in other words, the larger the gap G, and the smaller the protrusion amount, the more the screwing starts. Poor engagement at the time was likely to occur. On the other hand, the above-mentioned round corner portion 6 is intended to relatively rotate the nut by sliding with the opening edge portion of the nut. It has the function of correcting as much as possible the difference between the axes of each other until it becomes coaxial, making the two axes more concentric, and smoothly starting the screwing of both.

Next, a method of manufacturing the bolt 1 having the above-described rounded corner portion 6 will be described, first focusing on a change in the form from the material of the bolt to the product.

As shown in FIG. 6, the wire is cut into a simple shaft-shaped bolt material 46 (a), and then the end of the bolt material 46 on the side where the radius corner portion 6 is provided is tapered. Tapered portion 42 (taper angle is, for example, 10 to 30)
Degree) is forged (b). Further, as shown in (c), a head preformed portion 51
Is forged so as to have a larger diameter than the other shaft portions. Also,
At the end opposite to this, the taper angle of the above-mentioned tapered portion 42 is further increased (for example, the taper angle is, for example, about 40 to 50 degrees, particularly about 45 degrees), and the axial corner dimension is also reduced. The forming part 43 is forged.

At this time, the axial dimension of the round corner preformed portion 43 is the same as that of the round corner portion 6 shown in FIGS.
And the outer peripheral surface of the preformed portion 43 has a conical surface shape, or a radius of curvature r of the final rounded corner portion 6.
It can also be formed into a spherical shape with a radius of curvature larger than c.

Then, as shown in (d), the portion of the bolt shaft portion where the male screw is to be formed is formed as a rolled lower diameter portion 20 prior to thread rolling so as to be thinner than the other bolt shaft portions. Forging. The diameter of the rolled lower diameter portion 20 is substantially the same as the effective diameter of the final male screw portion, and the bolt shaft portion on which no male screw is formed is substantially the same as the screw outer diameter of the male screw portion. The round corner preform 43 is further forged to form a spherical final round corner 6 having a radius rc.
At the same time, a flat surface (shaft end face) 49 substantially perpendicular to the bolt axis is also forged. Are corner 6
Is made to smoothly contact the effective diameter of the screw. Also, the bolt head 2 is forged to its final form by this stage (before thread rolling). The stepwise process of forging the bolt head (a detailed process from the preforming portion 51 to the bolt head 2) is omitted.

Then, as shown in (e), the thread is formed by rolling so that the screw end is located with the middle of the radius corner 6 as a starting point or an end point, and the effective screw diameter of the rolling thread and the radius corner are formed. The starting point or the ending point of the part 6 will substantially coincide. By this thread rolling, a final bolt 1 is formed. As shown in an enlarged view in FIG. 7, the screw end is located in the middle of the round corner section 6, and the spherical round corner is determined from the effective screw diameter of the rolled thread section. Part 6 has begun (or can be said to be over).

FIG. 8 shows the steps shown in FIG. 6 together with a schematic cold forging apparatus.
Step (d) corresponds to steps (a) to (d) in FIG. 8A to 8D, a first die 71 to 73 (for example, an upper die) and a second die 81 to 83 (for example, a lower die) are used as a cold forging device. First mold 71
To 73 include mold bodies 71a to 73a, and the first mold 7
1 and 72 are provided with punches 71b and 72b, and
The molds (lower molds) 81 to 83 are provided with mold main bodies 81a to 83a and punches 81b to 83b.

In the step (a), the wire is cut into a bolt material 46. In (b), the bolt material 46 is subjected to cold forging by punches 71b and 81b, and the tapered portion shown in FIG. 42 is formed. In (c), the punch 7
2b and 82b give the form of the head preform 51 and the corner preform 43, and (d)
In the step, the first die 73, the second die 83, and the punch 8
3b (also a part of the second mold) forms a small-diameter portion 53 (thread-rolling lower-diameter portion) for thread rolling and a round corner portion 6 at the tip of the bolt shaft portion.
And a flat (or predetermined curved surface) bolt tip surface 5
Is formed.

As a forging die used in the forging step shown in FIG. 8D, for example, as shown in FIG. 9, a curvature for transferring the radius corner portion 6 to the bolt intermediate product 46 is formed on the inner surface of the die 83a. A forging die having a concave spherical forging surface 62 with a radius rc can be used. When the die 86a is filled with the bolt intermediate product 46 and is hit or pressed in the bolt axis direction by the punch 83b, the flesh of the bolt intermediate product 46 escapes and comes into close contact with the concave spherical forged surface 42, and the surface is pressed. The image is transferred to the shaft end of the bolt intermediate product 46 and the punch 83
The flat end surface of b forms the shaft end surface 5 at the end following the round corner portion 6. This round corner portion 6 is formed at the tip of the thread rolling lower diameter portion 20 set to the effective screw diameter db as described above, and the other bolt shaft portions correspond to the screw outer diameter da. It is assumed.

Instead of the forging die 83a shown in FIG. 9, instead of a concave spherical forming surface 62 for transferring the round corner portion 6, a relief 63 for forging as shown in FIG. 10 is provided. In the case of forging, the flesh of the bolt
3. A forging die 83a 'that forms a convex curved R-shaped portion (R') 6 '(which may not be an accurate spherical shape) by projecting outward so as to protrude outward.
Can also be used.

By the way, the following can be said as a more preferable embodiment of the bolt 1 in which the above-described round corner portion 6 (6 ') is formed. For example, when the protrusion amount of the guide extension portion (guide protruding portion) 7 in the screw axis direction is L (see FIGS. 2 to 4 and the like), and the radius of curvature of the round corner portion 6 of the guide extension portion 7 is rc, L / Rc is desirably 0.65 to 1.5.

When the diameter of the flat surface 5 formed at the end of the guide extension 7 is φ, rc / φ is preferably 0.15 to 0.35, and L / φ is also 0. .15
It is desirable to set it to 0.35. Further, the above L,
Regarding rc and φ, L: rc: φ is 3 to 5: 3 to 5: 1
It is preferably from 4 to 18. In addition, guide extension 6
The surface roughness of the rounded corners of (10 point average roughness is Rz
It is recommended to be 0.3 to 12.5 Rz.

By setting the ratio within the above range, a good guide function (such as an axis matching function) for the nut and the like of the rounded corner portion 6 and an effect of improving the durability against the above-mentioned dents and the like are synergistically obtained.

In order to evaluate from another aspect, FIG.
1, the pitch of the male screw portion 8 of the bolt 1 is P, the radius of curvature of the round corner portion 6 is rc, and the round corner portion 6 is
Is an angle with respect to a reference line (reference plane) C1 perpendicular to the bolt axis at the first end, and β is an angle with respect to a reference line (reference plane) C2 parallel to the bolt axis at the second end of the rounded corner portion 6. Here, a generally possible range of each value, a desirable range usually adopted, and an optimum value are as follows.

With respect to α, the generally possible range is from 0 to ±
It can be said that the preferable range is 0 to ± 20 °, and the optimum value is about α = 0 °. Regarding β, a generally possible range is ± 20 ° to ± 30 °, a desirable range usually adopted is 0 to ± 20 °, and an optimum value is about β = 0 °. Further, with respect to rc, the generally possible range is P to
3P, a desirable range usually adopted is 1.5P to 2.5
P, the optimal value can be said to be about rc = 2P. In other words, the radius of curvature rc of the rounded corner portion 6 is equivalent to about 1 to 3 pitches of the pitch P of the external thread, preferably 1.5 to 2.5 pitches, and particularly preferably about 2 pitches. It is recommended that

If the radius of curvature rc of the radius corner portion 6 is too small, the radius corner portion 6 remaining after the formation of the screw is formed.
Portion becomes very small, and it becomes difficult to obtain the above-described guide function for the nut and the like. On the contrary, even if rc is too large (curvature is small), screwing is performed from a state where the axis is relatively inclined. Therefore, it is difficult to obtain a function of rotating a nut or the like so as to correct it. Therefore, it is desirable to determine the range or the value as described above. For α and β,
If the values in the minus direction become large and the formation angle range of the rounded corner portion 6 becomes much less than 90 °, the above-described guide function for the nut and the like becomes insufficient, and conversely, the plus direction of α and β Becomes large,
When the formation angle range of the round corner portion 6 greatly exceeds 90 °, a discontinuous step may be generated between the round corner portion 6 and the lower diameter portion of the thread rolling or the flat surface of the tip of the bolt shaft portion, which is preferable. Absent.

In the above description, a general bolt is taken as an example. However, the present invention can be applied to all bolts without heads, stud bolts, and other shaft bolts having male threads. The bolt here is synonymous with a male screw member.

Further, forging in the bolt manufacturing method is as follows.
Although the description has been given on the assumption of cold forging, hot forging, warm forging, or the like may be used depending on conditions such as the type, size, and purpose of use of the bolt.

[Brief description of the drawings]

FIG. 1 is a view showing a bolt according to an embodiment of the present invention.

FIG. 2 is an enlarged view showing a main part of FIG. 1;

FIG. 3 is a diagram conceptually showing the position and form of a round corner portion in FIG. 2;

FIG. 4 is a diagram showing a modification of FIG. 2;

FIG. 5 is a diagram conceptually illustrating a guide function of a round corner portion.

FIG. 6 is a diagram illustrating an example of a bolt manufacturing process of FIG. 1 focusing on a work form for each process.

FIG. 7 is an enlarged view of a main part of the bolt obtained through the step of FIG. 6;

FIG. 8 is a view schematically showing an example of a forging device suitable for performing the step of FIG. 6;

FIG. 9 is a view showing an example of a forging die that can be employed in the forging apparatus of FIG. 8;

FIG. 10 is a diagram showing a modification of FIG. 9;

FIG. 11 is a diagram illustrating a preferred form of forming a round corner portion.

FIG. 12 is a view for explaining a conventional bolt in comparison with a bolt of the present invention having a rounded corner.

FIG. 13 is a view showing a conventional example in which guide projections are formed in a two-stage shaft shape from the end of a bolt shaft.

[Explanation of symbols]

 DESCRIPTION OF SYMBOLS 1 Bolt 3 Bolt shaft part 5 Shaft end face (flat surface) 6, 6 'R corner part 7 Guide extension part 8 Male screw part

 ────────────────────────────────────────────────── ─── Continuing on the front page (72) Inventor Hiroshi Kurauchi 22 Miyatsukoshi, Teratsu-cho, Nishio-shi, Aichi F-term in Sugiura Works (reference) 4E087 AA08 CA11 CA33 CB03 CC01 DB04 DB08 DB24 EC11 HA53

Claims (13)

[Claims] 1. A guide extension having a rounded corner portion whose diameter is gradually reduced in an arc-shaped cross section from an outer diameter substantially equal to the effective screw diameter or the outer diameter of the screw is formed at a tip end of the bolt, and the rounded corner of the guide extended portion is formed. A bolt having a thread formed such that a screw end comes in the middle of a portion. 2. A guide extension having a rounded corner portion whose diameter is gradually reduced in an arc shape in cross section from an outer diameter substantially equal to the effective screw diameter or the outer diameter of the screw is formed at a tip end of the bolt, and the rounded corner of the guide extended portion is formed. A screw thread is formed so that a screw end comes in the middle of the portion, and a tip end surface substantially coinciding with the end of the rounded corner portion of the guide extension is a flat surface substantially perpendicular to the screw axis. Bolt to do. 3. The L / r is 0.65 to 1.5, where L is the amount of protrusion of the guide extension in the screw axis direction and r is the radius of curvature of the radius corner.
Or the bolt according to 2. 4. When the pitch of the male screw of the bolt is P and the radius of curvature of the rounded corner portion is r, r is P to 3P.
The bolt according to any one of claims 1 to 3, wherein the bolt is set to a range of 1.5P to 2.5P. 5. The radius of curvature of the radius corner portion is r,
When the diameter of the flat surface is φ, r / φ is 0.15
The bolt according to any one of claims 2 to 4, wherein the bolt is set to 0.35. 6. When the amount of protrusion of the guide extension in the screw axis direction is L, the radius of curvature of the rounded corner of the guide extension is r, and the diameter of the flat surface of the guide extension is φ, L: The bolt according to any one of claims 2 to 6, wherein r: φ is 3 to 5: 3 to 5:14 to 18. 7. The method according to claim 1, wherein a surface roughness Rz (ten-point average roughness) of a round corner portion of the guide extension portion is 0.3 to 12.5. bolt. 8. A guide extension portion having a round corner portion whose diameter gradually decreases in an arc shape in section from an outer diameter approximately equal to the effective diameter of the screw or the outer diameter of the screw is formed in advance at the tip of the bolt intermediate member before forming the screw. A method of manufacturing a bolt, characterized in that a screw thread is formed by leaving a round corner portion partially so that a screw end comes to the middle of the round corner portion of the guide extension. 9. A front end portion of a bolt intermediate member before forming a screw has a round corner portion that gradually reduces in diameter in an arc-shaped cross section from an outer diameter substantially equal to the effective screw diameter or the outer diameter of the screw, and the round corner portion. A guide extension is formed in advance so that the tip surface substantially coincident with the end of the guide extension is a flat surface substantially perpendicular to the screw axis, and the rounded corner portion is positioned so that the screw end comes in the middle of the rounded corner portion of the guide extended portion. Forming a thread while partially leaving a thread. 10. A forging along with a bolt body portion, a guide extension portion having a rounded corner portion whose diameter is gradually reduced in an arc-shaped cross section from an outer diameter substantially equal to the effective screw diameter at the tip of the bolt intermediate member before thread rolling. A method for manufacturing a bolt, which is formed in advance by processing, and rolls a thread while partially leaving a round corner so that a screw end comes to the middle of the round corner of the guide extension. 11. A forging process, together with a bolt body portion, at a tip end portion of a bolt intermediate member before thread cutting, the guide extension portion having a round corner portion whose diameter is gradually reduced in an arc shape in cross section from an outer diameter substantially equal to the outer diameter of the screw. A method of manufacturing a bolt, wherein a thread is cut while leaving a rounded corner part partially so that a screw end comes to the middle of the rounded corner of the guide extension. 12. The ratio L / r is set to 0.65 to 1.5, where L is the amount of protrusion of the guide extension in the screw axis direction, and r is the radius of curvature of the rounded corner. 12. The method for manufacturing a bolt according to any one of claims 11 to 11. 13. When the pitch of the male screw of the bolt is P and the radius of curvature of the rounded corner portion is r, r is P to 3
The bolt manufacturing method according to any one of claims 8 to 12, wherein the range is set to a range of P or a range of 1.5P to 2.5P.