US3425354A - Centrifugally armed fuze - Google Patents

Centrifugally armed fuze Download PDF

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US3425354A
US3425354A US678910A US3425354DA US3425354A US 3425354 A US3425354 A US 3425354A US 678910 A US678910 A US 678910A US 3425354D A US3425354D A US 3425354DA US 3425354 A US3425354 A US 3425354A
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fuze
slider
fluid
rotation
axis
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Donovan Carlson
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Honeywell Inc
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    • FMECHANICAL ENGINEERING; LIGHTING; HEATING; WEAPONS; BLASTING
    • F42AMMUNITION; BLASTING
    • F42CAMMUNITION FUZES; ARMING OR SAFETY MEANS THEREFOR
    • F42C15/00Arming-means in fuzes; Safety means for preventing premature detonation of fuzes or charges
    • F42C15/18Arming-means in fuzes; Safety means for preventing premature detonation of fuzes or charges wherein a carrier for an element of the pyrotechnic or explosive train is moved
    • F42C15/184Arming-means in fuzes; Safety means for preventing premature detonation of fuzes or charges wherein a carrier for an element of the pyrotechnic or explosive train is moved using a slidable carrier
    • FMECHANICAL ENGINEERING; LIGHTING; HEATING; WEAPONS; BLASTING
    • F42AMMUNITION; BLASTING
    • F42CAMMUNITION FUZES; ARMING OR SAFETY MEANS THEREFOR
    • F42C15/00Arming-means in fuzes; Safety means for preventing premature detonation of fuzes or charges
    • F42C15/28Arming-means in fuzes; Safety means for preventing premature detonation of fuzes or charges operated by flow of fluent material, e.g. shot, fluids
    • F42C15/285Arming-means in fuzes; Safety means for preventing premature detonation of fuzes or charges operated by flow of fluent material, e.g. shot, fluids stored within the fuze housing

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  • centrifugal arming is quite well-known in the prior art. Most centrifugal arming arrangements, however, comprised of mechanical locks and weights. Fluid is utilized in some cases for the purpose of delaying the operation of the fuze. Examples of the prior art are Patents 2,641,186 to Apotheloz and 3,118,379 to Jasse. The applicant is not, however, aware of any prior art wherein fluid is used as a positive force in the arming sequence of a centrifugally armed fuze.
  • the present invention provides for an arming and time delay mechanism for spin operated fuzes. Its unique feature is that it employs a buoyant slider member mounted in a fluid-filled housing. In the unarmed condition the slider member is held away from the axis of rotation by a spring and by centrifugal looks or other suitable safing mechanisms. The space around the slider member is filled with a fluid having long-term stability and a relatively uniform viscosity over a broad temperature range. The fluid has adequate density to float the slider assembly.
  • the fuze is spin actuated.
  • the centrifugal locks are released under spin environment, releasing the slider member.
  • the fluid is displaced outwardly, away from the axis of rotation, and the buoyant slider is forced by the fluid inwardly toward the axis of rotation.
  • the slider member carries an explosive detonator, which upon actuation is carried by the slider member into a position in line with a firing pin and a pyrotechnic chain.
  • a further object of the present invention is to provide a centrifugally armed fuze wherein a fluid is used to provide a positive force in the arming sequence.
  • FIGURE 1 is a cross-sectional view of a typical embodiment of the fuze according to the present invention, looking along the spin axis from the top of the fuze;
  • FIGURE 2 is a simplified schematic representation of the embodiment of FIGURE 1;
  • FIGURE 3 is a sectional side view taken along line 3-3 of FIGURE 1;
  • FIGURE 4 is a simplified schematic. representation of the sectional side view of FIGURE 3.
  • FIGURE 5 is a similar sectional side view, but with the fuze in the armed position.
  • FIGURE 1 a cross-sectional view of the fuze is shown out along a plane perpendicular to the axis of rotation.
  • the fuze has an outside fuze housing 10.
  • a delay housing 12 Within fuze housing 10 is mounted a delay housing 12.
  • Delay housing 12 defines a cylindrical cavity -13 whose axis intersects the axis of rotation and lies in a plane substantially perpendicular to the axis of rotation. Cavity 13 extends from one side of housing 10 across the center of housing 10, a certain distance beyond the axis of rotation.
  • Within cavity 13 is mounted a buoyant slider piston 14.
  • Slider piston 14 is biased towards the end of cavity 13 which is nearest the outside wall of housing 10. The biasing is accomplished by a light spring 15 located between slider piston 14 and a closure member 16 which defines the inner end of delay housing 12.
  • Slider piston 14 carries a detonator 18 at a position which is away from the axis of rotation while the slider piston is in its normal position adjacent to the outside wall of housing 10.
  • the entire internal cavity of delay housing 12 is filled with a fluid 20.
  • Fluid 20 is chosen for a long-term stability and a relatively uniform viscosity over a broad temperature range.
  • the relative density of fluid 20 to slider piston 14 is such that slider piston 14 will float.
  • the slider piston can be provided with a hollow cavity 21, such as shown in FIGURE 1. Cavity 21 is shown being sealed by a cover 22.
  • seal 17 is placed around the periphery of slider'member 14, adjacent to the internal walls of delay housing 20.
  • the purpose of seal 17 is to prevent uncontrolled flow of fluid 20 from one side to the other side of slider piston 14.
  • a metering orifice 19 is, however, provided to allow the flow of fluid 20 from one side to the other side of slider piston 14 at a controlled rate.
  • a pair of centrifugal locks 24 and 25 are mounted within delay housing 12 and are adapted to engage with slider piston 14 to prevent the motion of piston 14 prior to a predetermined threshold of angular rotation about the fuze axis of rotation.
  • FIG- URE 3 shows a cross-section of a side view cut along lines 3-3 of FIGURE 1.
  • Delay housing 12 is shown held between a forward housing member 28 and a rear housing member 29.
  • An opening 30 is formed in forward housing member 28, opening 32 being centrally located and coaxial with opening 30 on rear housing member 29.
  • Mounted within opening 32 is a firing pin 34.
  • Firing pin 34 has a first flange 35 formed adjacent the pointed end thereof, to prevent the firing pin 18 from being forced out of opening 17.
  • a second flange 36 is connected to the opposite end of firing pin 34 by a screw 37.
  • a coiled spring 38 which tends to hold firing pin 34 in the position shown in FIGURE 3.
  • buoyant slider piston 14, carrying detonator 18, is held away from the axis of rotation by centrifugal locks 24 and 25. If redundancy is desired for additional safety, setback locks can also be added although they are not shown in the embodiments of FIGURES 1 and 2.
  • the space surrounding slider piston 14 is filled with a fluid such as Dow Corning Silicone 200, which has a long-term stability, has a relatively uniform viscosity over a broad temperature range, and is of adequate density to float slider piston 14.
  • the displacement away from the axis of rotation of lock weights of centrifugal locks 24 and 25 under the spin environment releases slider piston 14. Under spin conditions the fluid is displaced outwardly through orifice 19 at a rate de pending on rotational velocity and orifice size. The resulting buoyant force acting on the slider member moves it toward the in-line position against a light return spring 15.
  • Delay time will depend on the viscosity of the fluid and hence on temperature.
  • the use of a very short orifice causes the flow rate to follow the Bernoulli equation, and minimizes the flow restriction due to the viscous shearforces, thus yielding a delay that is inversely proportional to the spin rate and relatively insensitive to temperature.
  • the delay time can be controlled by varying the spring biasing and varying viscosity of the fluid.
  • centrifugal locks are shown in FIGURE 1 for holding the slider prior to the operation of the fuze, these may not be necessary because of the force-time integrating features of the dash-pot system.
  • a setback lock pin may be more appropriate.
  • a unique feature of the present invention is that in case of loss of fluid from the system, the fuze will remain in a fail-safe condition. This is an advantage of great importance, as will be obvious to those who are familiar with the safety hazards in the area of fuzing art.
  • An arming and time delay mechanism for spin operated fuzes comprising:
  • a fuze housing defining a hermetically sealed chamber filled with a relatively high density fluid
  • a buoyant slider positioned in said fluid within said chamber, said slider having a freedom of motion along a line substantially perpendicular to the spin axis of the fuze;
  • locking means mounted in said housing for holding said slider away from the axis of rotation when said fuze is in an unarmed condition, and to release said slider for motion toward the axis of rotation in response to fluid pressure exerted on said slider, in line with a firing pin and pyrotechnic chain, after the fuze is subjected to an angular rotation.
  • An arming and time delay mechanism for a spin operated munition fuze comprising:
  • a fuze housing having an axis of rotation
  • a firing pin and an explosive lead cup mounted in said housing centered on said axis of rotation;
  • a delay housing mounted within said fuze housing, said delay housing defining a hollow hermetically sealed chamber of generally cylindrical shape with its axis substantially perpendicular to said axis of rotation;
  • a slideable piston member mounted within said delay housing, said piston member subdividing the sealed chamber of said delay housing into a first chamber toward said axis of rotation and a second chamber away from said axis of rotation, said piston member further having a fluid passage to allow fluid transfer between said two chambers;
  • safing means mounted in said delay housing for holding said piston member away from the axis of rotation when said fuze is in an unarmed state, and to allow said piston member to move toward the axis of rotation when said fuze is caused to spin about its axis of rotation in response to fluid flow from said first chamber to said second chamber to arm the fuze by bringing said detonator in line with said firing pin and said explosive lead cup.
  • said safing means further includes centrifugal locking means for maintaining said slideable piston locked in a safe position until said fuze is caused to spin about its axis of rotation in excess of a predetermined angular rate.

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Description

Feb. 4, 1969 o. CARLSON 3,425,354
GENTRIFUGALLY ARMED FUZ E Filed Oct. 30, 1967 I NVENTOR. DONOVAN CARLSON AT TORNE Y 3,425,354 CENTRIFUGALLY ARMED FUZE Donovan Carlson, Minneapolis, Minn., assignor to Honeywell Inc., Minneapolis, Minn., a corporation of Delaware Filed Oct. 30, 1967, Ser. No. 678,910 US. Cl. 10279 Int. Cl. F42c 9/06, 15/26 4 Claims ABSTRACT OF THE DISCLOSURE Background of the invention Field of the invention.Percussive or electric fuzes wherein the fuze is armed by inovement of a member which responds centrifugally to rotation of the shell (CL 102-79).
Description of the prior art.Centrifugal arming is quite well-known in the prior art. Most centrifugal arming arrangements, however, comprised of mechanical locks and weights. Fluid is utilized in some cases for the purpose of delaying the operation of the fuze. Examples of the prior art are Patents 2,641,186 to Apotheloz and 3,118,379 to Jasse. The applicant is not, however, aware of any prior art wherein fluid is used as a positive force in the arming sequence of a centrifugally armed fuze.
Summary of the invention The present invention provides for an arming and time delay mechanism for spin operated fuzes. Its unique feature is that it employs a buoyant slider member mounted in a fluid-filled housing. In the unarmed condition the slider member is held away from the axis of rotation by a spring and by centrifugal looks or other suitable safing mechanisms. The space around the slider member is filled with a fluid having long-term stability and a relatively uniform viscosity over a broad temperature range. The fluid has adequate density to float the slider assembly.
The fuze is spin actuated. The centrifugal locks are are released under spin environment, releasing the slider member. Under the spin conditions, the fluid is displaced outwardly, away from the axis of rotation, and the buoyant slider is forced by the fluid inwardly toward the axis of rotation. The slider member carries an explosive detonator, which upon actuation is carried by the slider member into a position in line with a firing pin and a pyrotechnic chain.
It is therefore an object of the present invention to provide an improved centrifugally armed fuze. A further object of the present invention is to provide a centrifugally armed fuze wherein a fluid is used to provide a positive force in the arming sequence. These and further objects will become apparent to those skilled in the art upon examination of the following specification, claims, and the drawing.
A brief description of the drawing FIGURE 1 is a cross-sectional view of a typical embodiment of the fuze according to the present invention, looking along the spin axis from the top of the fuze;
States Patent 3,425,354 Patented Feb. 4, 1969 FIGURE 2 is a simplified schematic representation of the embodiment of FIGURE 1;
FIGURE 3 is a sectional side view taken along line 3-3 of FIGURE 1;
FIGURE 4 is a simplified schematic. representation of the sectional side view of FIGURE 3; and
FIGURE 5 is a similar sectional side view, but with the fuze in the armed position.
Detailed description Referring now to FIGURE 1, a cross-sectional view of the fuze is shown out along a plane perpendicular to the axis of rotation. The fuze has an outside fuze housing 10. Within fuze housing 10 is mounted a delay housing 12. Delay housing 12 defines a cylindrical cavity -13 whose axis intersects the axis of rotation and lies in a plane substantially perpendicular to the axis of rotation. Cavity 13 extends from one side of housing 10 across the center of housing 10, a certain distance beyond the axis of rotation. Within cavity 13 is mounted a buoyant slider piston 14. Slider piston 14 is biased towards the end of cavity 13 which is nearest the outside wall of housing 10. The biasing is accomplished by a light spring 15 located between slider piston 14 and a closure member 16 which defines the inner end of delay housing 12.
Slider piston 14 carries a detonator 18 at a position which is away from the axis of rotation while the slider piston is in its normal position adjacent to the outside wall of housing 10. The entire internal cavity of delay housing 12 is filled with a fluid 20. Fluid 20 is chosen for a long-term stability and a relatively uniform viscosity over a broad temperature range. The relative density of fluid 20 to slider piston 14 is such that slider piston 14 will float. To give slider piston 14 sufiicient buoyancy, the slider piston can be provided with a hollow cavity 21, such as shown in FIGURE 1. Cavity 21 is shown being sealed by a cover 22.
At the inner most end of slider piston 14, a seal 17 is placed around the periphery of slider'member 14, adjacent to the internal walls of delay housing 20. The purpose of seal 17 is to prevent uncontrolled flow of fluid 20 from one side to the other side of slider piston 14. A metering orifice 19 is, however, provided to allow the flow of fluid 20 from one side to the other side of slider piston 14 at a controlled rate.
A pair of centrifugal locks 24 and 25 are mounted Within delay housing 12 and are adapted to engage with slider piston 14 to prevent the motion of piston 14 prior to a predetermined threshold of angular rotation about the fuze axis of rotation.
A more clear understanding of the apparatus of FIG- URE 1 will be achieved by referring to FIGURE 3. FIG- URE 3 shows a cross-section of a side view cut along lines 3-3 of FIGURE 1. Delay housing 12 is shown held between a forward housing member 28 and a rear housing member 29. Formed in the rear housing member 29, concentric with the axis of rotation, is an opening 30 within which is located a lead cup or booster charge 31. An opening 32 is formed in forward housing member 28, opening 32 being centrally located and coaxial with opening 30 on rear housing member 29. Mounted within opening 32 is a firing pin 34. Firing pin 34 has a first flange 35 formed adjacent the pointed end thereof, to prevent the firing pin 18 from being forced out of opening 17. A second flange 36 is connected to the opposite end of firing pin 34 by a screw 37. Mounted between flange 36 and forward housing member 28 is a coiled spring 38 which tends to hold firing pin 34 in the position shown in FIGURE 3.
The simplified schematics of views 2, 4, and 5 will be helpful in understanding the operation of the invention.
Operation In the unarmed condition, buoyant slider piston 14, carrying detonator 18, is held away from the axis of rotation by centrifugal locks 24 and 25. If redundancy is desired for additional safety, setback locks can also be added although they are not shown in the embodiments of FIGURES 1 and 2. The space surrounding slider piston 14 is filled with a fluid such as Dow Corning Silicone 200, which has a long-term stability, has a relatively uniform viscosity over a broad temperature range, and is of adequate density to float slider piston 14. The displacement away from the axis of rotation of lock weights of centrifugal locks 24 and 25 under the spin environment releases slider piston 14. Under spin conditions the fluid is displaced outwardly through orifice 19 at a rate de pending on rotational velocity and orifice size. The resulting buoyant force acting on the slider member moves it toward the in-line position against a light return spring 15.
Delay time will depend on the viscosity of the fluid and hence on temperature. The use of a very short orifice causes the flow rate to follow the Bernoulli equation, and minimizes the flow restriction due to the viscous shearforces, thus yielding a delay that is inversely proportional to the spin rate and relatively insensitive to temperature. The delay time can be controlled by varying the spring biasing and varying viscosity of the fluid.
Although centrifugal locks are shown in FIGURE 1 for holding the slider prior to the operation of the fuze, these may not be necessary because of the force-time integrating features of the dash-pot system. A setback lock pin may be more appropriate.
A unique feature of the present invention, as compared to prior art fluid delays, is that in case of loss of fluid from the system, the fuze will remain in a fail-safe condition. This is an advantage of great importance, as will be obvious to those who are familiar with the safety hazards in the area of fuzing art.
The following functioning sequence places the fuze from a unarmed to an armed position. Centrifugal locks 24 and 25 are released by centrifugal forces above a safety threshold. Fluid 20 is displaced radially through metering orifice 19 by a centrifugal force at a rate dependent upon projectile spin and orifice size. The slider floats toward armed position, snapping in line when seal 17 passes over arming grooves 40 and 41, thus permitting a sudden increase in fluid flow rate.
Obvious advantages of the present invention are that it is extremely simple in operation and is therefore highly reliable. It has the unique safety feature that it is impossible to prematurely arm and has high resistance to rough handling environments.
From the above description it will be apparent that I have invented a munition fuzing concept having new and more effective means for utilizing the centrifugal force developed by a rotation munition for arming purposes and providing safety in handling.
I claim:
1. An arming and time delay mechanism for spin operated fuzes comprising:
a fuze housing defining a hermetically sealed chamber filled with a relatively high density fluid;
a buoyant slider positioned in said fluid within said chamber, said slider having a freedom of motion along a line substantially perpendicular to the spin axis of the fuze;
an explosive detonator mounted on said slider; and
locking means mounted in said housing for holding said slider away from the axis of rotation when said fuze is in an unarmed condition, and to release said slider for motion toward the axis of rotation in response to fluid pressure exerted on said slider, in line with a firing pin and pyrotechnic chain, after the fuze is subjected to an angular rotation.
2. An arming and time delay mechanism for a spin operated munition fuze comprising:
a fuze housing having an axis of rotation;
a firing pin and an explosive lead cup mounted in said housing centered on said axis of rotation;
a delay housing mounted within said fuze housing, said delay housing defining a hollow hermetically sealed chamber of generally cylindrical shape with its axis substantially perpendicular to said axis of rotation;
a slideable piston member mounted within said delay housing, said piston member subdividing the sealed chamber of said delay housing into a first chamber toward said axis of rotation and a second chamber away from said axis of rotation, said piston member further having a fluid passage to allow fluid transfer between said two chambers;
a fluid filling said sealed chamber of said delay housing, said fluid having suflicicnt density to float said piston member;
a detonator mounted on said piston member; and
safing means mounted in said delay housing for holding said piston member away from the axis of rotation when said fuze is in an unarmed state, and to allow said piston member to move toward the axis of rotation when said fuze is caused to spin about its axis of rotation in response to fluid flow from said first chamber to said second chamber to arm the fuze by bringing said detonator in line with said firing pin and said explosive lead cup.
3. Apparatus according to claim 2 wherein said safing means includes a spring for biasing said piston member away from the axis of rotation.
4. Apparatus according to claim 3, wherein said safing means further includes centrifugal locking means for maintaining said slideable piston locked in a safe position until said fuze is caused to spin about its axis of rotation in excess of a predetermined angular rate.
References Cited UNITED STATES PATENTS 527,250 10/ 1894 Smith 102-82 3,118,379 1/1964 Jasse 102-79 3,264,995 8/1966 Libby et al 102-79 3,296,969 1/ 1967 Mueller et a1. 102-82 FOREIGN PATENTS I 129,041 7/ 1919 Great Britain.
BENJAMIN A. BORCHELT, Primary Examiner. GERALD H. GLANZMAN, Assistant Examiner.
US. Cl. X.R. 102-82
US678910A 1967-10-30 1967-10-30 Centrifugally armed fuze Expired - Lifetime US3425354A (en)

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Cited By (12)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
US3633511A (en) * 1968-11-13 1972-01-11 Lacroix E Rocket fuse with delayed-action arming
US3640225A (en) * 1969-06-20 1972-02-08 Honeywell Inc Fuze apparatus
US3721195A (en) * 1971-06-01 1973-03-20 Honeywell Inc Liquid revolution counter for fuze arming
US3732824A (en) * 1971-04-28 1973-05-15 Us Army Means for converting impulse linear acceleration to rotational inertia
US3750589A (en) * 1971-12-13 1973-08-07 Honeywell Inc Centrifugally driven spin device
US4018164A (en) * 1973-09-10 1977-04-19 Breed Corporation Projectile fuze containing a floating body
US4078497A (en) * 1971-06-30 1978-03-14 Breed Corporation Liquid timing device having a floating mass
US4098192A (en) * 1974-05-15 1978-07-04 Breed David S Ball rotor safety and arming delay device
US4213395A (en) * 1974-05-15 1980-07-22 Breed David S Ball rotor safety and arming delay device
US7530312B1 (en) 2006-06-14 2009-05-12 Sandia Corporation Inertial sensing microelectromechanical (MEM) safe-arm device
CN112556518A (en) * 2020-11-23 2021-03-26 南京理工大学 Small-caliber ammunition micro-fluid fuse security mechanism
CN113932665A (en) * 2021-07-08 2022-01-14 南京理工大学 Explosion-proof mechanism of rotary bullet detonator

Families Citing this family (1)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
DE3446098A1 (en) * 1984-12-18 1986-06-26 Gebrüder Junghans GmbH, 7230 Schramberg BULLET IGNITION

Citations (5)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
US527250A (en) * 1894-10-09 Time-fuse for projectiles
GB129041A (en) * 1917-10-03 1919-07-10 Walter Gordon Wilson Improvements in and relating to Fuses for Projectiles.
US3118379A (en) * 1960-11-23 1964-01-21 Fuze for a gyratory projectile
US3264995A (en) * 1964-05-11 1966-08-09 Avco Corp Mechanical fuze operable on grazing impact
US3296969A (en) * 1964-10-14 1967-01-10 Thiokol Chemical Corp Time delay initiator

Patent Citations (5)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
US527250A (en) * 1894-10-09 Time-fuse for projectiles
GB129041A (en) * 1917-10-03 1919-07-10 Walter Gordon Wilson Improvements in and relating to Fuses for Projectiles.
US3118379A (en) * 1960-11-23 1964-01-21 Fuze for a gyratory projectile
US3264995A (en) * 1964-05-11 1966-08-09 Avco Corp Mechanical fuze operable on grazing impact
US3296969A (en) * 1964-10-14 1967-01-10 Thiokol Chemical Corp Time delay initiator

Cited By (14)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
US3633511A (en) * 1968-11-13 1972-01-11 Lacroix E Rocket fuse with delayed-action arming
US3640225A (en) * 1969-06-20 1972-02-08 Honeywell Inc Fuze apparatus
US3732824A (en) * 1971-04-28 1973-05-15 Us Army Means for converting impulse linear acceleration to rotational inertia
US3721195A (en) * 1971-06-01 1973-03-20 Honeywell Inc Liquid revolution counter for fuze arming
US4078497A (en) * 1971-06-30 1978-03-14 Breed Corporation Liquid timing device having a floating mass
US3750589A (en) * 1971-12-13 1973-08-07 Honeywell Inc Centrifugally driven spin device
US4018164A (en) * 1973-09-10 1977-04-19 Breed Corporation Projectile fuze containing a floating body
US4098192A (en) * 1974-05-15 1978-07-04 Breed David S Ball rotor safety and arming delay device
US4213395A (en) * 1974-05-15 1980-07-22 Breed David S Ball rotor safety and arming delay device
US7530312B1 (en) 2006-06-14 2009-05-12 Sandia Corporation Inertial sensing microelectromechanical (MEM) safe-arm device
CN112556518A (en) * 2020-11-23 2021-03-26 南京理工大学 Small-caliber ammunition micro-fluid fuse security mechanism
CN112556518B (en) * 2020-11-23 2022-03-22 南京理工大学 Small-caliber ammunition micro-fluid fuse security mechanism
CN113932665A (en) * 2021-07-08 2022-01-14 南京理工大学 Explosion-proof mechanism of rotary bullet detonator
CN113932665B (en) * 2021-07-08 2023-04-28 南京理工大学 Explosion-proof mechanism of rotary bullet fuze

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SE357257B (en) 1973-06-18
DE1805427A1 (en) 1969-06-19
CH495548A (en) 1970-08-31

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