Laminated-glass intermediate film, rolled body, laminated glass, and method for producing laminated glass
11565507 · 2023-01-31
Assignee
Inventors
Cpc classification
B32B17/10807
PERFORMING OPERATIONS; TRANSPORTING
B32B17/10036
PERFORMING OPERATIONS; TRANSPORTING
International classification
Abstract
The present invention aims to provide an interlayer film for laminated glass which, while having recesses in the shape of engraved lines, enables the production of a laminated glass with high production efficiency by a nip roll method; a roll of the interlayer film for laminated glass; a laminated glass including the interlayer film for laminated glass; and a method of producing laminated glass. The present invention relates to an interlayer film for laminated glass. The interlayer film includes, on at least one surface thereof, a large number of recesses and a large number of projections. The recesses have a groove shape with a continuous bottom. The recesses are adjacently arranged regularly side by side in parallel with one another. The recesses in a groove shape with a continuous bottom are inclined 55° or less relative to the machine direction of the film in production of the interlayer film for laminated glass.
Claims
1. An interlayer film for laminated glass, the interlayer film comprising, on at least one surface thereof: recesses; and projections, the recesses having a groove shape with a continuous bottom, the recesses being adjacently arranged regularly side by side in parallel with one another, the recesses having a groove shape with a continuous bottom being inclined at 55° or less relative to a machine direction, wherein the machine direction is determined by storing the interlayer film for laminated glass in a constant-temperature bath at 140° C. for 30 minutes and then determining whether a parallel direction or a perpendicular direction has a greater shrinkage after the storing, the machine direction being either the parallel direction or the perpendicular direction that has the greater shrinkage, wherein the projections each have a tip with a radius of rotation of 20 μm or more, and wherein tip portions of the projections have a roughness of 30 μm or less.
2. A roll obtained by winding the interlayer film for laminated glass according to claim 1 in the machine direction of the film in production of the interlayer film for laminated glass.
3. A laminated glass, comprising: a pair of glass plates; and the interlayer film for laminated glass according to claim 1 between the glass plates.
4. A method of producing a laminated glass by a nip roll method: the method comprising transporting a laminate including at least two glass plates and the interlayer film for laminated glass of claim 1 therebetween such that the recesses in a groove shape with a continuous bottom of the interlayer film for laminated glass are inclined at 550 or less relative to a flow direction of the conveyer.
5. The interlayer for laminated glass according to claim 1, wherein the interlayer film comprises an upper surface and a lower surface, wherein both the upper surface and the lower surface comprise the recesses and the projections, and wherein the recesses and the projections of the upper surface and the recesses and the projections of the lower surface extend in a same direction.
Description
BRIEF DESCRIPTION OF DRAWINGS
(1)
(2)
(3)
(4)
DESCRIPTION OF EMBODIMENTS
(5) The embodiments of the present invention are further described with reference to example. The present invention is not limited to the examples.
Examples 1 to 4
Comparative Examples 1 and 2
(1) Preparation of Interlayer Film for Laminated Glass
(6) Polyvinyl alcohol having an average degree of polymerization of 1700 was acetalized with n-butylaldehyde to prepare polyvinyl butyral (acetyl group content: 1 mol %, butyral group content: 69 mol %, hydroxy group content: 30 mol %). To 100 parts by mass of the polyvinyl butyral were added 40 parts by mass of triethyleneglycol-di-2-ethylhexanoate (3GO) as a plasticizer and a 50% by mass: 50% by mass mixture of magnesium bis(2-ethyl butyrate) and magnesium acetate as an adhesion modifier in such an amount that the magnesium concentration in the film was 50 ppm. The mixture was sufficiently kneaded with a mixing roll. Thus, a resin composition was obtained.
(7) The obtained resin composition was extruded with an extruder, whereby a single-layer interlayer film for laminated glass with a thickness of 760 μm was obtained.
(8) In the first step, a pattern of projections and recesses was randomly transferred to both surfaces of the interlayer film for laminated glass by the following process. First, random projections and recesses were formed on the surface of iron rolls with an abrasive material, and the iron rolls were subjected to vertical grinding. Finer projections and recesses were further formed on planar portions after the grinding with a finer abrasive material. In this manner, a pair of rolls in the same shape having a coarse main embossed pattern and a fine sub-embossed pattern was obtained. The pair of rolls was used as a device for transferring a pattern of projections and recesses to transfer a random pattern of projections and recesses to both surfaces of the interlayer film. The transferring conditions employed here were a temperature of the interlayer film for laminated glass of 80° C., a temperature of the rolls of 145° C., a linear velocity of 10 m/min, and a linear pressure of 10 to 200 kN/m.
(9) In the second step, projections and recesses having a groove shape with a continuous bottom (shape of an engraved line) were imparted to a surface of the interlayer film for laminated glass by the following process. A pair of rolls including a metal roll having a surface milled with a triangular oblique line-type mill and a rubber roll having a JIS hardness of 65 to 75 was used as a device for transferring a pattern of projections and recesses. The obtained interlayer film for laminated glass was passed through the device for transferring a pattern of projections and recesses, whereby projections and recesses in which recesses having a groove shape with a continuous bottom (shape of an engraved line) were arranged side by side in parallel with one another at equal intervals were imparted to one surface (surface A) of the interlayer film for laminated glass such that the recesses having groove shape with a continuous bottom were inclined at 55° or less relative to the machine direction of the film. Specifically, the inclination of the recesses was 10° in Example 1, 35° in Example 2, 45° in Example 3, 55° in Example 4, 70° in Comparative Example 1, and 90° in Comparative Example 2. The transferring was performed under the conditions of a temperature of the interlayer film for laminated glass of 70° C., a roll temperature of 145° C., a linear velocity of 10 m/min, and a linear pressure of 5 to 100 kN/m.
(10) Subsequently, the same treatment was performed to impart recesses having a groove shape with a continuous bottom (shape of an engraved line) to the other surface (surface B) of the interlayer film for laminated glass. The direction of the recesses in the shape of engraved lines of the surface B was the same as that of the surface A.
(11) The film thickness after the formation of engraved lines was measured. The film thickness in the width direction and the machine direction was 760 μm. The difference between the maximum thickness and the minimum thickness was 26 μm. The thickness profile was divided at 15 cm intervals in the measurement direction, and the difference between the maximum thickness and the minimum thickness in each section was recorded. The difference was 12 μm in the section where the difference was largest.
(2) Evaluation of Projections and Recesses of Interlayer Film for Laminated Glass
(12) In accordance with JIS B-0601 (1994), the roughness (Rz) of the recesses in the shape of engraved lines on each of the surfaces A and B of the obtained interlayer film for laminated glass was determined. The measurement direction was perpendicular to the engraved lines. Measurement was performed under the conditions of a cut-off value of 2.5 mm, a standard length of 2.5 mm, evaluation length of 12.5 mm, a tip radius of a stylus of 2 μm, a tip angle of 60°, and a measurement rate of 0.5 mm/s.
(13) The interval of the recesses in the shape of engraved lines was determined as follows. Each of the surfaces A and B of the interlayer film for laminated glass was observed at five sites (observation range: 20 mm×20 mm) with an optical microscope (BS-D8000 III produced by SONIC Corp.), and the shortest distances between deepest bottoms of observed adjacent recesses were measured. The average of the measured shortest distances was taken as the interval.
(14) The interlayer film for laminated glass was cut in the direction perpendicular to the direction of the recesses in the shape of engraved lines and perpendicular to the film thickness. The cross section was observed with a microscope (“DSX-100” available from Olympus Corp.). The cross section was photographed at a 555-fold magnification. The obtained image was magnified to 50 μm/20 mm. In the magnified state, the radius of a circle drawn such that it was inscribed in the apex of a projection was measured as the radius of rotation of the projection.
(3) Evaluation of Roughness of Tip Portions of Projections
(15) The roughness of the tip portions of the projections was determined as follows. Using a three-dimensional profilometer (“KS-1100” available from Keyence Corporation, head: model “LT-9510VM”), the shape of the surface A and the surface B of the interlayer films for laminated glass obtained in examples and comparative examples was measured in a measurement range of 20 mm×20 mm. The resulting data was processed with “KS-measure”, measurement software included with the profilometer. Thus, three-dimensional image data of the surface A and surface B was obtained.
(16) In the obtained data, the roughness within a length of 2.5 mm along the direction parallel to the direction in which the apex portions of the projections were continuous was measured using “KS-Analyzer Ver. 2.00”, analysis software included with the profilometer, in the line roughness measurement mode, so that roughness profile data was obtained. In the same manner, roughness profile data of 10 sites was obtained from the three-dimensional image data. Here, the roughness profile data was obtained at a cut-off value of 2.5 mm. Height smoothing and tilt correction were not performed. The Rz was calculated from the obtained roughness profile data in accordance with JIS B-0601 (1994). The average of the Rz values obtained from the roughness profile data of 10 sites was taken as the roughness of the tip portions of the projections.
(17) The measurement conditions other than the field of view were as follows: stage feed condition: continuous; scan direction: bi-directional scanning; leading axis: X-axis; stage travel rate: 250.0 μm/s; and axis feed rate: 10000.0 μm/s. The measuring pitch of X-axis is set at 2.0 μm, and that of Y-axis is set at 2.0 μm. When the interval between the engraved lines was so large that the measurement distance was insufficient, a field of view adjacent to the measured field of view was measured in the same manner to increase the number of measurement sites. The “apex portion” of a projection in the measurement of the roughness of the tip portion is defined as follows. If the point at which the height of the projection is highest is positioned at the middle of a straight line connecting the deepest bottoms of two adjacent recesses in the 2 cm×2 cm field of view, the apex portion is a range corresponding to 10% of the length of the straight line connecting the deepest bottoms, centered on the middle of the straight line. If the point at which the height of the projection is highest is not positioned at the middle of the straight line connecting the deepest bottoms of two adjacent recesses in the 2 cm×2 cm field of view, the apex portion is a range corresponding to 10% of the length of the straight line connecting the deepest bottoms, centered on the point at which the height of the projection is highest. The maximum height point of the projections was measured as follows. A cross-sectional profile in the direction perpendicular to the recesses in the obtained image was obtained. The profile was corrected by performing height smoothing (weighted average±12) to remove fine projections and recesses. The maximum point of the projections in the corrected profile was taken as the heights of projections.
(18) The measurement results of the surface A of the interlayer film for laminated glass are shown in Table 1. The measurement results of the surface B were the same as those of the surface A and thus are omitted in the table.
(4) Measurement of Friction Between Glass and Interlayer Film for Laminated Glass
(19) The obtained interlayer film for laminated glass was allowed to stand at 23° C. and 50% RH for six hours to perform humidity control.
(20) Thereafter, the interlayer film for laminated glass was placed on a horizontal, smooth bench with the surface A upward. Five float glass plates (7.5 cm long×7.5 cm wide×about 2.5 mm high) that complied with JIS R3202:1996 were laminated on the interlayer film. The five float glass sheets were bonded to each other and fixed together. The total weight of the five float glass plates thus laminated was 176 g. Iron wire having a length of 15 cm with a ring attached to one end was fixed with tape to the top surface of the glass plate such that the wire extended from the middle portion of the top surface toward the direction parallel to the machine direction of the film in the production of the interlayer film. A spring balance was hooked to the ring. The glass used was float glass and was placed such that the tin-contact side was in contact with the interlayer film. The glass was used after washing so that no plasticizer or foreign matter was attached thereto. The surface roughness of the glass was 0.013 μm, as measured with “Serfcorder SE300” available from Kosaka Laboratory Ltd. The measurement conditions were in accordance with those for the roughness “Rz” of the recesses of the film. The arithmetic average roughness “Ra” as measured under the same conditions was 0.065 μm.
(21) With the interlayer film for laminated glass being fixed, the spring balance was pulled at 6 cm/s in the direction that was the horizontal direction and parallel to the machine direction of the film in the production of the interlayer film. The value displayed by the spring balance during the glass plate moved at a constant rate was recorded. This procedure was repeated five times. The average of the five measurements was taken as friction between the glass and the interlayer film. When the glass rolled on the interlayer film during the glass plate moved at a constant rate, the procedure was redone. The measurement was performed at 23° C. and 30RH %.
(22) Table 1 shows the results.
(23) TABLE-US-00001 TABLE 1 Comparative Comparative Example 1 Example 2 Example 3 Example 4 Example 1 Example 2 Composition of Polyvinyl Average degree of 1700 1700 1700 1700 1700 1700 interlayer film butyral resin polymerization of PVA Degree of mol % 69 69 69 69 69 69 butyralization Degree of mol % 1 1 1 1 1 1 acetylation Hydroxy group mol % 30 30 30 30 30 30 content Amount Parts by 100 100 100 100 100 100 mass Plasticizer Type 3GO 3GO 3GO 3GO 3GO 3GO Amount Parts by 40 40 40 40 40 40 mass Shape of Interval between recesses μm 290 290 290 290 290 290 projections and Roughness of recesses in the μm 36 36 36 36 36 36 recesses shape of engraved lines Radius of rotation of tip portion μm 28 28 28 28 28 28 Roughness of tip portions μm 14 14 14 14 14 14 Inclination of recesses in the degree 10 35 45 55 70 90 shape of engraved lines relative to (° ) machine direction of interlayer film in production of the film Glass/interlayer film friction (g) 220 180 180 170 140 120
Examples 5 to 7
Comparative Examples 3 and 4
(24) An interlayer film for laminated glass was obtained and the friction between the glass and the interlayer film for laminated glass was measured in the same manner as in Example 1, except that the shape of the projections and recesses imparted to the film was changed by changing the shape of the embossing rolls in the first step, the triangular oblique line-type roll, and the inclination of the recesses having a groove shape with a continuous bottom relative to the machine direction of the film.
(25) Table 2 shows the results.
(26) TABLE-US-00002 TABLE 2 Comparative Comparative Example 5 Example 6 Example 7 Example 3 Example 4 Composition of Polyvinyl Average degree of 1700 1700 1700 1700 1700 interlayer film butyral resin polymerization of PVA Degree of mol % 69 69 69 69 69 butyralization Degree of mol % 1 1 1 1 1 acetylation Hydroxy group mol % 30 30 30 30 30 content Amount Parts by 100 100 100 100 100 mass Plasticizer Type 3GO 3GO 3GO 3GO 3GO Amount Parts by 40 40 40 40 40 mass Shape of Interval between recesses μm 292 292 292 290 290 projections and Roughness of recesses in the μm 42 42 42 55 55 recesses shape of engraved lines Radius of rotation of tip portion μm 55 55 55 28 28 Roughness of tip portions μm 20 20 20 14 14 Inclination of recesses in the degree 10 45 55 70 90 shape of engraved lines relative to (° ) machine direction of interlayer film in production of the film Glass/interlayer film friction (g) 220 190 180 140 120
Examples 8 to 11
Comparative Example 5
(27) An interlayer film for laminated glass was obtained and the friction between the glass and the interlayer film for laminated glass was measured in the same manner as in Example 1, except that the shape of the projections and recesses imparted to the film was changed by changing the shape of the embossing rolls in the first step, the triangular oblique line-type roll, and the inclination of the recesses having a groove shape with a continuous bottom relative to the machine direction of the film.
(28) Table 3 shows the results.
(29) TABLE-US-00003 TABLE 3 Comparative Example 8 Example 9 Example 10 Example 11 Example 5 Polyvinyl Average degree of 1700 1700 1700 1700 1700 butyral resin polymerization of PVA Degree of mol % 69 69 69 69 69 butyralization Degree of mol % 1 1 1 1 1 acetylation Hydroxy group mol % 30 30 30 30 30 content Amount Parts by 100 100 100 100 100 mass Plasticizer Type 3GO 3GO 3GO 3GO 3GO Amount Parts by 40 40 40 40 40 mass Shape of Interval between recesses μm 380 380 380 380 380 projections and Roughness of recesses in the μm 45 45 45 45 45 recesses shape of engraved lines Radius of rotation of tip portion μm 30 30 30 30 30 Roughness of tip portions μm 12 12 12 12 12 Inclination of recesses in the degree 10 35 45 55 90 shape of engraved lines relative to (° ) machine direction of interlayer film in production of the film Glass/interlayer film friction (g) 220 200 180 170 150
Examples 12 to 14
Comparative Examples 6 and 7
(30) An interlayer film for laminated glass was obtained and the friction between the glass and the interlayer film for laminated glass was measured in the same manner as in Example 1, except that the shape of the projections and recesses imparted to the film and the inclination of the recesses having a groove shape with a continuous bottom relative to the machine direction of the film were changed by changing the triangular oblique line-type mill.
(31) Table 4 shows the results.
(32) TABLE-US-00004 TABLE 4 Comparative Comparative Example 12 Example 13 Example 14 Example 6 Example 7 Composition of Polyvinyl Average degree of 1700 1700 1700 1700 1700 interlayer film butyral resin polymerization of PVA Degree of mol % 69 69 69 69 69 butyralization Degree of mol % 1 1 1 1 1 acetylation Hydroxy group mol % 30 30 30 30 30 content Amount Parts by 100 100 100 100 100 mass Plasticizer Type 3GO 3GO 3GO 3GO 3GO Amount Parts by 40 40 40 40 40 mass Shape of Interval between recesses μm 416 416 416 416 416 projections and Roughness of recesses in the μm 31 31 31 31 31 recesses shape of engraved lines Radius of rotation of tip portion μm 50 50 50 50 50 Roughness of tip portions μm 0.2 0.2 0.2 0.2 0.2 Inclination of recesses in the degree 10 45 55 70 90 shape of engraved lines relative to (° ) machine direction of interlayer film in production of the film Glass/interlayer film friction (g) 280 210 200 160 140
Examples 15 to 17
Comparative Example 8
(33) An interlayer film for laminated glass was obtained and the friction between the glass and the interlayer film for laminated glass was measured in the same manner as in Example 1, except that the shape of the projections and recesses imparted to the film and the inclination of the recesses having a groove shape with a continuous bottom relative to the machine direction of the film were changed by changing the shape of the embossing rolls in the first step and the triangular oblique line-type mill.
(34) Table 5 shows the results.
(35) TABLE-US-00005 TABLE 5 Comparative Example 15 Example 16 Example 17 Example 8 Composition of Polyvinyl Average degree of 1700 1700 1700 1700 interlayer film butyral resin polymerization of PVA Degree of mol % 69 69 69 69 butyralization Degree of mol % 1 1 1 1 acetylation Hydroxy group mol % 30 30 30 30 content Amount Parts by 100 100 100 100 mass Plasticizer Type 3GO 3GO 3GO 3GO Amount Parts by 40 40 40 40 mass Shape of Interval between recesses μm 396 396 390 389 projections and Roughness of recesses in the μm 31 31 31 31 recesses shape of engraved lines Radius of rotation of tip portion μm 85 85 85 85 Roughness of tip portions μm 25 25 25 25 Inclination of recesses in the degree 10 45 55 70 shape of engraved lines relative to (° ) machine direction of interlayer film in production of the film Glass/interlayer film friction (g) 200 180 180 140
Examples 18 to 22
Comparative Example 9
(36) An interlayer film for laminated glass was obtained and the friction between the glass and the interlayer film for laminated glass was measured in the same manner as in Example 1, except that the shape of the projections and recesses imparted to the film and the inclination of the recesses having a groove shape with a continuous bottom relative to the machine direction of the film were changed by changing the shape of the embossing rolls in the first step and the triangular oblique line-type mill.
(37) Table 6 shows the results.
(38) TABLE-US-00006 TABLE 6 Comparative Example 18 Example 19 Example 20 Example 21 Example 22 Example 9 Composition of Polyvinyl Average degree of 1700 1700 1700 1700 1700 1700 interlayer film butyral resin polymerization of PVA Degree of mol % 69 69 69 69 69 69 butyralization Degree of mol % 1 1 1 1 1 1 acetylation Hydroxy group mol % 30 30 30 30 30 30 content Amount Parts by 100 100 100 100 100 100 mass Plasticizer Type 3GO 3GO 3GO 3GO 3GO 3GO Amount Parts by 40 40 40 40 40 40 mass Shape of Interval between recesses μm 178 180 180 185 185 185 projections and Roughness of recesses in the μm 42 42 42 55 36 36 recesses shape of engraved lines Radius of rotation of tip portion μm 51 50 50 22 60 60 Roughness of tip portions μm 13 13 13 13 13 13 Inclination of recesses in the degree 20 35 45 35 55 80 shape of engraved lines relative to (° ) machine direction of interlayer film in production of the film Glass/interlayer film friction (g) 220 210 200 200 180 160
Examples 23 to 26
Comparative Example 10
(39) The step of “(1) Preparation of interlayer film for laminated glass” in Example 1 was changed as follows.
(40) (Preparation of Resin Composition for Protective Layer)
(41) Polyvinyl alcohol having an average degree of polymerization of 1700 was acetalized with n-butylaldehyde to prepare polyvinyl butyral (acetyl group content: 1 mol %, butyral group content: 69 mol %, hydroxy group content: 30 mol %). To 100 parts by mass of the polyvinyl butyral were added 40 parts by mass of triethyleneglycol-di-2-ethylhexanoate (3GO) as a plasticizer and a 50% by mass: 50% by mass mixture of magnesium bis(2-ethylbutyrate) and magnesium acetate as an adhesion modifier in such an amount that the magnesium concentration in the film was 50 ppm. The mixture was sufficiently kneaded with a mixing roll. Thus, a resin composition for protective layer was obtained.
(42) (Preparation of Resin Composition for Sound Insulation Layer)
(43) Polyvinyl alcohol having an average degree of polymerization of 2300 was acetalized with n-butyraldehyde to prepare polyvinyl butyral (acetyl group content of 12 mol %, butyral group content of 64 mol %, hydroxy group content of 24 mol %). To 100 parts by mass of the obtained polyvinyl butyral was added 60 parts by mass of triethylene glycol-di-2-ethylhexanoate (3GO) as a plasticizer. The mixture was sufficiently kneaded with a mixing roll. Thus, a resin composition for sound insulation layer was obtained.
(44) (Preparation of Interlayer Film for Laminated Glass)
(45) The obtained resin composition for sound insulation layer and the resin composition for protective layer were co-extruded from a co-extruder to produce an interlayer film for laminated glass having a triple layer structure in which a first surface layer (protective layer) formed of the resin composition for protective layer, an intermediate layer (sound insulation layer) formed of the resin composition for sound insulation layer, and a second surface layer (protective layer) formed of the resin composition for protective layer were laminated in the stated order.
(46) In the subsequent steps, an interlayer film for laminated glass was prepared and the friction between glass and the interlayer film for laminated glass was measured in the same manner as in Example 1, except that the shape of the projections and recesses imparted to the film and the inclination of the recesses having a groove shape with a continuous bottom relative to the machine direction of the film were changed by changing the shape of embossing rolls in the first step and the triangular oblique line-type mill among the conditions for preparing the interlayer film for laminated glass.
(47) Table 7 shows the results.
(48) TABLE-US-00007 TABLE 7 Comparative Example 23 Example 24 Example 25 Example 26 Example 10 Composition of Polyvinyl Average degree of 1700 1700 1700 1700 1700 protective layer butyral resin polymerization of PVA Degree of mol % 69 69 69 69 69 butyralization Degree of mol % 1 1 1 1 1 acetylation Hydroxy group mol % 30 30 30 30 30 content Amount Parts by 100 100 100 100 100 mass Plasticizer Type 3GO 3GO 3GO 3GO 3GO Amount Parts by 40 40 40 40 40 mass Composition of Polyvinyl Average degree of 2300 2300 2300 2300 2300 sound insulation butyral resin polymerization of layer PVA Degree of mol % 64 64 64 64 64 butyralization Degree of mol % 12 12 12 12 12 acetylation Hydroxy group mol % 24 24 24 24 24 content Amount Parts by 100 100 100 100 100 mass Plasticizer Type 3GO 3GO 3GO 3GO 3GO Amount Parts by 60 60 60 60 60 mass Shape of Interval between recesses μm 290 290 290 290 290 projections and Roughness of recesses in the μm 36 36 36 36 36 recesses shape of engraved lines Radius of rotation of tip portion μm 28 28 28 28 28 Roughness of tip portions μm 14 14 14 14 14 Inclination of recesses in the degree 10 35 45 55 70 shape of engraved lines relative to (° ) machine direction of interlayer film in production of the film Glass/interlayer film friction (g) 220 180 180 170 140
INDUSTRIAL APPLICABILITY
(49) The present invention provides an interlayer film for laminated glass which, while having recesses in the shape of engraved lines, enables the production of laminated glass with high production efficiency by a nip roll method; a roll of the interlayer film for laminated glass; a laminated glass including the interlayer film for laminated glass; and a method of producing laminated glass.
REFERENCE SIGNS LIST
(50) 1 recess 2 recess 3 recess A interval between recess 1 and recess 2 B interval between recess 1 and recess 3 20 projections and recesses on surface having a large number of recesses and a large number of projections 21 recess having a groove shape with a continuous bottom 22 projection R radius of rotation of tip of projection