Senz Magnet's Ferrite Ring Magnet

In todays fast-paced industrial environment, productivity is key. Ferrite arc magnets have become a game-changing solution, offering both efficiency and reliability. These magnets, known for their high coercivity and low production cost, have a wide range of applications across various industries.

AbstractFerrite arc magnets are composed of ferrite, a material with distinct magnetic properties. The arc process enhances their magnetic strength and durability. The core shapes, designed to optimize magnetic flux, play a crucial role in their functionality. Surrounding material ensures high coercivity, making these magnets highly effective and reliable.

Applications of Ferrite Arc Magnets in IndustryFerrite arc magnets find extensive use in several industries. In conveyor systems, they ensure smooth operation and consistent magnetic attraction. In lifting equipment, their durability and strength make them ideal for handling heavy loads. Additionally, in electromagnetic separators, they efficiently separate materials based on magnetic properties. These applications leverage the unique strengths of ferrite arc magnets, contributing to overall productivity and efficiency.

Comparative Analysis: Ferrite Arc Magnets vs. Other Magnetic MaterialsWhen comparing ferrite arc magnets to other magnetic materials like neodymium and alnico, several factors come into play. Ferrite magnets offer lower production costs and better reliability, making them a cost-effective choice. Neodymium magnets, however, provide higher magnetic strength, which may be preferable in certain applications. Alnico magnets, known for their versatility, strike a balance between cost and performance. Understanding these trade-offs helps in selecting the right magnetic solution for specific needs.

Practical Success Stories with Ferrite Arc MagnetsSeveral industries have successfully implemented ferrite arc magnets, achieving notable improvements. For instance, a manufacturing plant upgraded its conveyor systems, leading to reduced maintenance costs and increased throughput. Another company integrating ferrite magnets in lifting equipment experienced enhanced reliability and efficiency. These case studies highlight the tangible benefits of ferrite arc magnets in real-world applications.

Maintenance and Care for Ferrite Arc MagnetsProper maintenance is crucial for maximizing the lifespan of ferrite arc magnets. Regular cleaning, proper handling, and avoiding harsh environmental conditions are essential. Environmental factors such as temperature and humidity can impact performance, so maintaining optimal conditions is key to ensuring longevity and efficiency.

Future Trends and Advancements in Ferrite Arc Magnet TechnologyLooking ahead, advancements in ferrite magnet technology promise further innovations. Researchers are exploring new materials and processes to enhance performance, durability, and cost-effectiveness. Emerging trends include the development of high-performance ferrite compounds and smarter magnetic solutions that adapt to changing conditions, paving the way for even greater productivity in the future.

Leveraging Ferrite Arc Magnets for Enhanced ProductivityFerrite arc magnets are a game-changer in industrial applications, offering unmatched productivity and efficiency. From reducing maintenance costs to improving reliability, their impact is profound. By embracing ferrite arc magnets, industries can elevate their operations, drive innovation, and achieve sustainable growth. Encouraging their adoption is not just a technological leap but a strategic move towards future success.
By addressing the feedback and making the necessary adjustments, the article is now more concise, engaging, and easier to read while maintaining its comprehensive and professional nature.

Ferrite magnets, as a cost-effective and versatile magnetic material, are widely utilized across multiple industries due to their unique properties, including corrosion resistance, temperature stability, and adaptability in shape and size. Below is a detailed analysis of their primary applications, supported by specific examples:

1. Automotive Industry
Ferrite magnets play a crucial role in automotive systems, particularly in components requiring durability and cost-efficiency:


Electric Power Steering (EPS) Systems: Ferrite magnets are used in the rotor assemblies of EPS motors, providing stable magnetic fields for precise steering control. Their resistance to demagnetization ensures long-term reliability.
Automotive Sensors: Ferrite magnets are integrated into sensors for detecting wheel speed, crankshaft position, and camshaft timing. For instance, in anti-lock braking systems (ABS), ferrite-based sensors monitor wheel rotation to prevent skidding.
Under-the-Hood Components: Ferrite magnets are employed in alternators, starters, and fuel injectors, where their high-temperature tolerance (up to 250°C) and corrosion resistance are critical for engine compartment environments.

2. Consumer Electronics
The consumer electronics sector leverages ferrite magnets for their affordability and sufficient magnetic strength for everyday applications:


Audio Devices: In speakers, headphones, and microphones, ferrite magnets generate the magnetic field necessary to convert electrical signals into sound. For example, large-volume production of portable speakers relies on ferrite magnets due to their low cost and adequate performance.
Magnetic Latches and Sensors: Ferrite magnets are used in laptop lids, refrigerator doors, and cabinet closures to provide secure yet easy-to-open mechanisms. They also serve as reed switch actuators in smartphones and tablets for proximity sensing.
Educational Kits and Crafts: Ferrite magnets are popular in educational toys, such as magnetic building blocks, and DIY projects due to their safety (non-toxic) and ease of handling.

3. Electric Motors and Generators
Ferrite magnets are extensively used in motor and generator applications, particularly where cost and efficiency are prioritized over high magnetic strength:


Household Appliances: In washing machines, refrigerators, and air conditioners, ferrite magnets are used in the rotor assemblies of motors to drive compressors, fans, and pumps. Their low remanence ensures smooth operation and reduces energy consumption.
Power Tools: Cordless drills, saws, and grinders utilize ferrite magnets in their motors for cost-effective performance. For example, a typical cordless drill motor may use ferrite magnets to achieve a balance between power output and battery life.
Wind Turbines: Ferrite magnets are employed in the generators of small-scale wind turbines, where their resistance to demagnetization and ability to operate in varying temperatures make them suitable for renewable energy applications.

4. Telecommunications
In the telecommunications industry, ferrite magnets are valued for their high magnetic permeability and low electrical conductivity, which minimize signal interference:


Transformer Cores and Inductors: Soft ferrite magnets are used in the cores of transformers and inductors to efficiently transfer electrical energy while reducing losses. For instance, in power supplies for telecommunications equipment, ferrite cores ensure stable voltage regulation.
Antenna Systems: Ferrite magnets are integrated into antennas for mobile phones and base stations to improve signal reception and transmission. Their low conductivity prevents eddy current losses, enhancing overall system efficiency.

5. Magnetic Separation and Holding
Ferrite magnets are widely used in magnetic separation processes due to their corrosion resistance and low cost:


Industrial Magnetic Separators: In food processing, pharmaceuticals, and mining, ferrite magnets remove ferrous contaminants from liquids and powders. For example, in a cereal production line, ferrite magnets are installed in conveyor belts to capture metal fragments, ensuring product safety.
General-Purpose Holding Mechanisms: Ferrite magnets are used in magnetic chucks for holding workpieces during machining, as well as in magnetic bases for tools and gauges. Their strong holding force and durability make them ideal for workshop environments.

6. Refrigeration and HVAC Systems
Ferrite magnets are essential components in refrigeration and heating, ventilation, and air conditioning (HVAC) systems:


Fan Motors and Compressors: In refrigerators, air conditioners, and heat pumps, ferrite magnets are used in the motors of fans and compressors to drive airflow and cooling cycles. Their high-temperature tolerance ensures reliable operation in enclosed spaces.
Thermostats and Sensors: Ferrite magnets are integrated into thermostats and humidity sensors to control temperature and air quality. For example, in a smart thermostat, ferrite-based sensors monitor room conditions and adjust HVAC settings accordingly.

7. Medical Instruments
Ferrite magnets find applications in medical devices where non-toxicity and biocompatibility are important:


Magnetic Resonance Imaging (MRI) Machines: While MRI machines primarily use superconducting magnets, ferrite magnets are used in auxiliary components, such as gradient coils and shielding, to minimize magnetic interference.
Dental and Surgical Tools: Ferrite magnets are used in dental drills and surgical instruments for precise control and easy sterilization. Their corrosion resistance ensures they remain hygienic for repeated use.

8. Renewable Energy
Ferrite magnets contribute to the development of renewable energy technologies:


Solar Panel Tracking Systems: In solar farms, ferrite magnets are used in the motors of tracking systems that adjust the angle of solar panels to follow the sun’s path. This maximizes energy capture and improves overall efficiency.
Hydroelectric Generators: Ferrite magnets are employed in the generators of small hydroelectric plants, where their resistance to demagnetization and ability to operate in wet environments make them suitable for water-powered energy generation.

9. Smart Manufacturing and IoT
With the rise of smart manufacturing and the Internet of Things (IoT), ferrite magnets are finding new applications:


Position Sensors in Robotics: Ferrite magnets are used in the encoders of robotic arms to track their position and movement. This enables precise control in automated assembly lines and warehouse logistics.
Wireless Charging Systems: Ferrite magnets are integrated into wireless charging pads for smartphones and other devices to focus the magnetic field and improve charging efficiency. Their low conductivity reduces energy loss during transmission.

Aluminum-nickel-cobalt (AlNiCo) magnets, composed of a combination of aluminum (Al), nickel (Ni), cobalt (Co), iron (Fe), and sometimes other elements like copper (Cu) and titanium (Ti), are renowned for their excellent magnetic stability, high-temperature resistance, and wide range of applications. One of the key factors contributing to their versatility is the availability of various shapes, each tailored to specific functional requirements. This comprehensive guide explores the different shapes of AlNiCo magnets, their characteristics, manufacturing processes, and typical applications.

1. Standard Shapes of AlNiCo Magnets
1.1 Bar Magnets
Characteristics: Bar magnets are one of the most common and straightforward shapes of AlNiCo magnets. They are elongated rectangular prisms with a uniform cross-section along their length. The magnetic poles are typically located at the two ends of the bar, with one end being the north (N) pole and the other the south (S) pole.

Manufacturing Process: The production of bar magnets involves several steps. First, the raw materials (Al, Ni, Co, Fe, etc.) are melted in a furnace to form an alloy. The molten alloy is then poured into a mold with the desired bar shape and allowed to solidify. After solidification, the magnet is subjected to heat treatment processes, such as annealing and aging, to optimize its magnetic properties. Finally, the magnet is machined to achieve the precise dimensions and surface finish required for the application.

Applications: Bar magnets find applications in various fields. In educational settings, they are used to demonstrate basic magnetic principles, such as magnetic field lines and the interaction between magnetic poles. In industrial applications, they are employed in magnetic separators to remove ferrous contaminants from non-magnetic materials. Additionally, bar magnets are used in some types of sensors and switches where a simple magnetic field source is needed.

1.2 Rod Magnets
Characteristics: Rod magnets are similar to bar magnets but are generally longer and have a smaller diameter. They also have magnetic poles at their two ends. The elongated shape of rod magnets allows for a more focused and directional magnetic field along their length.

Manufacturing Process: The manufacturing process for rod magnets is comparable to that of bar magnets. The alloy is melted, poured into rod-shaped molds, solidified, heat-treated, and then machined to the required specifications. The length-to-diameter ratio can be adjusted during the mold design stage to meet different application needs.

Applications: Rod magnets are commonly used in applications where a strong and directional magnetic field is required over a relatively long distance. For example, in some types of magnetic levitation systems, rod magnets are used to create a stable magnetic field that supports and guides the levitating object. They are also used in magnetic stirrers in laboratories, where the rotating magnetic field generated by the rod magnet drives the stirring bar in the liquid sample.

1.3 Ring Magnets
Characteristics: Ring magnets have a circular cross-section and a central hole. They can be thought of as a hollow cylinder with magnetic properties. The magnetic poles can be arranged in different ways on ring magnets. In some cases, one face of the ring is the north pole, and the opposite face is the south pole (axial magnetization). In other cases, the magnetic poles are on the inner and outer circumferences of the ring (radial magnetization).

Manufacturing Process: To manufacture ring magnets, the molten AlNiCo alloy is poured into ring-shaped molds. After solidification, the magnets undergo heat treatment to enhance their magnetic performance. For radial magnetization, additional processes such as magnetizing in a specialized fixture with a radial magnetic field are required. Machining operations may be carried out to achieve the desired outer diameter, inner diameter, and thickness of the ring.

Applications: Ring magnets have a wide range of applications. In electric motors and generators, they are used as part of the rotor or stator assemblies to create a rotating magnetic field. The radial magnetization of some ring magnets makes them suitable for applications where a magnetic field needs to be concentrated around a central axis, such as in some types of magnetic couplings. In loudspeakers, ring magnets are used to provide a stable magnetic field for the voice coil, which helps in converting electrical signals into sound waves.

1.4 Disc Magnets
Characteristics: Disc magnets are flat, circular magnets with a relatively small thickness compared to their diameter. They have two flat faces, one of which is the north pole and the other the south pole (axial magnetization). Disc magnets can generate a strong magnetic field perpendicular to their flat surfaces.

Manufacturing Process: The production of disc magnets starts with melting the AlNiCo alloy and pouring it into disc-shaped molds. After solidification, heat treatment is applied to improve the magnetic properties. Machining operations, such as grinding and polishing, are then carried out to achieve the required surface finish and dimensional accuracy.

Applications: Disc magnets are widely used in various applications. In the automotive industry, they are used in sensors, such as speed sensors and position sensors, where their strong and focused magnetic field can be easily detected by magnetic sensors. In the electronics industry, disc magnets are used in magnetic switches and relays. They are also popular in consumer products, such as refrigerator magnets, where their flat shape allows for easy attachment to metal surfaces.

2. Specialized Shapes of AlNiCo Magnets
2.1 horseshoe Magnets
Characteristics: Horseshoe magnets have a distinctive U-shape, with the two poles (north and south) located at the open ends of the U. This shape allows the magnetic field lines to be concentrated between the two poles, creating a strong and focused magnetic field in the gap between them.

Manufacturing Process: Manufacturing horseshoe magnets involves melting the AlNiCo alloy and pouring it into a horseshoe-shaped mold. After solidification, heat treatment is performed to optimize the magnetic properties. The magnet may then be machined to achieve the desired dimensions and surface quality. In some cases, the two ends of the horseshoe may be further processed to enhance the magnetic field concentration, such as by beveling or rounding the edges.

Applications: Horseshoe magnets are commonly used in applications where a strong and localized magnetic field is required. In magnetic lifters, horseshoe magnets are used to lift and handle ferrous objects. The concentrated magnetic field between the poles allows for a secure grip on the object. They are also used in some types of magnetic chucks in metalworking machines, where they hold workpieces in place during machining operations. In educational settings, horseshoe magnets are used to demonstrate the concept of magnetic field concentration and the interaction between magnetic poles.

2.2 Cylindrical Magnets with Conical Ends
Characteristics: These magnets have a cylindrical body with conical ends. The conical ends can be designed to have different angles, which affects the distribution of the magnetic field. The magnetic field is stronger near the conical tips and gradually decreases towards the middle of the cylinder.

Manufacturing Process: The manufacturing process starts with creating a mold that has a cylindrical cavity with conical sections at both ends. The molten AlNiCo alloy is poured into this mold and allowed to solidify. Heat treatment is then carried out to improve the magnetic properties, followed by machining operations to achieve the precise dimensions and surface finish.

Applications: Cylindrical magnets with conical ends are used in applications where a non-uniform magnetic field is required. For example, in some types of magnetic sensors, the conical ends can be used to create a specific magnetic field gradient that is sensitive to changes in the position or orientation of a magnetic object. They are also used in some medical devices, where the focused magnetic field at the conical tips can be used for targeted magnetic stimulation or manipulation.

2.3 Custom-Shaped Magnets
Characteristics: Custom-shaped AlNiCo magnets are designed and manufactured according to specific application requirements. These shapes can be highly complex, incorporating features such as holes, slots, steps, and irregular contours. Custom-shaped magnets are tailored to fit into unique spaces or to interact with other components in a specific way to achieve the desired magnetic function.

Manufacturing Process: The manufacturing of custom-shaped magnets often involves computer-aided design (CAD) and computer-aided manufacturing (CAM) technologies. First, the desired shape is designed using CAD software, taking into account the magnetic requirements and the mechanical constraints of the application. The design is then used to create a mold or a machining program. For mold-based manufacturing, the mold is fabricated, and the molten AlNiCo alloy is poured into it. For machining-based manufacturing, a blank magnet is first produced (usually in a standard shape), and then it is machined into the custom shape using CNC (computer numerical control) machines. Heat treatment is applied as needed to optimize the magnetic properties, and final surface finishing operations are carried out.

Applications: Custom-shaped AlNiCo magnets are used in a wide range of high-tech and specialized applications. In aerospace, they may be used in guidance systems, where their unique shapes are designed to fit into compact spaces and provide precise magnetic fields for sensor operation. In the medical field, custom-shaped magnets can be used in magnetic resonance imaging (MRI) machines, where they are arranged in specific patterns to generate the required magnetic fields for imaging. In the automotive industry, custom-shaped magnets are used in advanced electric power steering systems and other electronic control systems, where their shapes are optimized for efficient magnetic coupling and signal transmission.

3. Factors Influencing the Choice of Magnet Shape
3.1 Magnetic Field Requirements
The desired magnetic field distribution is a crucial factor in determining the shape of the AlNiCo magnet. For applications requiring a strong and focused magnetic field in a specific area, shapes such as horseshoe magnets or cylindrical magnets with conical ends may be preferred. In applications where a more uniform magnetic field over a larger area is needed, disc or ring magnets with axial magnetization may be more suitable.

3.2 Space Constraints
The available space in the application also plays a significant role in shape selection. If the magnet needs to fit into a compact or irregularly shaped space, custom-shaped magnets may be the only option. Standard shapes like bar or rod magnets may be chosen when there is more flexibility in terms of space, and their simple shapes can be easily integrated into the overall design.

3.3 Mechanical Requirements
The mechanical properties of the magnet, such as its strength, durability, and ability to withstand vibrations and shocks, can also influence the shape selection. Some shapes may be more prone to breakage or damage under certain mechanical conditions. For example, thin disc magnets may be more fragile compared to thicker bar magnets. The shape should be chosen to ensure that the magnet can withstand the mechanical stresses it will be subjected to during operation.

3.4 Cost Considerations
The cost of manufacturing different shapes of AlNiCo magnets can vary significantly. Standard shapes are generally less expensive to produce because they can be mass-produced using standardized molds and manufacturing processes. Custom-shaped magnets, on the other hand, require more complex design, mold fabrication, and machining operations, which can increase the cost. The cost-benefit analysis should be carried out to determine whether the benefits of a custom shape justify the additional cost.

4. Conclusion
The variety of shapes available for AlNiCo magnets is a testament to their versatility and adaptability to a wide range of applications. From standard shapes like bar, rod, ring, and disc magnets to specialized shapes such as horseshoe magnets, cylindrical magnets with conical ends, and custom-shaped magnets, each shape offers unique magnetic properties and advantages. When selecting the shape of an AlNiCo magnet, it is essential to consider factors such as magnetic field requirements, space constraints, mechanical requirements, and cost considerations. By carefully evaluating these factors, engineers and designers can choose the most appropriate shape of AlNiCo magnet to ensure optimal performance and reliability in their specific applications. As technology continues to advance, it is likely that new and innovative shapes of AlNiCo magnets will be developed to meet the evolving needs of various industries.

Below is a comprehensive comparison of the four mainstream permanent magnets—Alnico, Ferrite, Neodymium Iron Boron (NdFeB), and Samarium Cobalt (SmCo)—covering their core properties, costs, temperature resistance, and application scenarios:

1. Alnico Magnets
Core Properties:


Composition: Aluminum (Al), Nickel (Ni), Cobalt (Co), Iron (Fe), and trace elements (e.g., copper, titanium).
Magnetic Performance:

Remanence (Br): 0.6–1.3 T (moderate).
Coercivity (Hc): 50–150 kA/m (low, prone to demagnetization).
Maximum Energy Product (BHmax): 5–50 kJ/m³ (low to moderate).


Temperature Stability:

Low reversible temperature coefficient: -0.02%/°C.
Operating Temperature: Up to 600°C (highest among permanent magnets).



Cost:


Moderate: Cheaper than SmCo and NdFeB but more expensive than ferrite.
Economical for high-temperature applications due to durability.

Temperature Resistance:


Exceptional: Maintains stability at temperatures exceeding 500°C, with a Curie temperature of ~850°C.

Application Scenarios:


High-Temperature Environments: Sensors, meters, and instruments requiring stable performance above 300°C.
Aerospace: Actuators and motors in jet engines or spacecraft.
Electric Guitars: Pickups (due to low coercivity and warm tonal characteristics).
Magnetic Teaching Aids and Crafts: Low magnetic strength suits safe, interactive applications.

2. Ferrite Magnets
Core Properties:


Composition: Strontium (Sr) or Barium (Ba) ferrite (SrFe₁₂O₁₉ or BaFe₁₂O₁₉).
Magnetic Performance:

Remanence (Br): 0.2–0.4 T (low).
Coercivity (Hc): 150–300 kA/m (moderate).
Maximum Energy Product (BHmax): 10–40 kJ/m³ (low).


Temperature Stability:

High Curie Temperature: ~450°C.
Stable across wide temperature ranges (-40°C to 250°C).



Cost:


Lowest: Abundant raw materials (Fe₂O₃) and simple manufacturing reduce costs.
Cost-effective for mass-produced consumer goods.

Temperature Resistance:


Good: Resistant to thermal degradation but may lose magnetism near Curie temperature.

Application Scenarios:


Consumer Electronics: Speakers, microphones, and refrigerator door seals.
Automotive: Motors, sensors, and alternators.
Power Supplies: Transformers and inductors (due to high electrical resistance).
Magnetic Closures: Cabinets, toys, and crafts (low cost and safety).

3. Neodymium Iron Boron (NdFeB) Magnets
Core Properties:


Composition: Neodymium (Nd), Iron (Fe), Boron (B), and trace elements (e.g., dysprosium for temperature stability).
Magnetic Performance:

Remanence (Br): 1.0–1.4 T (highest).
Coercivity (Hc): >1000 kA/m (high resistance to demagnetization).
Maximum Energy Product (BHmax): 280–550 kJ/m³ (highest, up to 10× ferrite).


Temperature Stability:

Moderate: Operating temperature up to 220°C (standard grades); high-temperature grades (e.g., N52SH) tolerate 250°C.
Curie Temperature: ~320–460°C.



Cost:


High: Rare-earth elements (Nd, Dy) increase cost, but cheaper than SmCo.
Cost-performance balance: Strongest magnet per unit volume.

Temperature Resistance:


Limited: Performance degrades above 150°C unless specially stabilized.

Application Scenarios:


Electric Vehicles (EVs): Traction motors, EPS (Electric Power Steering), and regenerative braking.
Wind Turbines: Direct-drive generators (high efficiency and compact size).
Consumer Electronics: Smartphones, headphones, and vibration motors.
Medical Devices: MRI machines (compact, high-field magnets).
Robotics: High-precision servo motors.

4. Samarium Cobalt (SmCo) Magnets
Core Properties:


Composition: Samarium (Sm), Cobalt (Co), and trace elements (e.g., iron, copper, zirconium).
Magnetic Performance:

Remanence (Br): 0.8–1.1 T (high).
Coercivity (Hc): 400–800 kA/m (high resistance to demagnetization).
Maximum Energy Product (BHmax): 160–320 kJ/m³ (moderate to high).


Temperature Stability:

Excellent: Operating temperature up to 350°C (2:17 type); some grades tolerate 500°C.
Curie Temperature: ~700–850°C.



Cost:


Highest: Rare-earth elements (Sm, Co) and complex manufacturing drive costs.
Justified for extreme environments where NdFeB fails.

Temperature Resistance:


Superior: Maintains performance at temperatures where NdFeB degrades.

Application Scenarios:


Aerospace: Satellite actuators, missile guidance systems, and jet engine sensors.
Military: High-temperature motors and underwater equipment.
Medical: MRI machines (alternative to NdFeB for high-temperature stability).
Industrial: High-performance motors, generators, and oil/gas drilling equipment.

Comparative Summary




Parameter
Alnico
Ferrite
NdFeB
SmCo




Remanence (Br)
0.6–1.3 T
0.2–0.4 T
1.0–1.4 T
0.8–1.1 T


Coercivity (Hc)
50–150 kA/m
150–300 kA/m
>1000 kA/m
400–800 kA/m


BHmax
5–50 kJ/m³
10–40 kJ/m³
280–550 kJ/m³
160–320 kJ/m³


Max Temp
600°C
250°C
220–250°C
350–500°C


Cost
Moderate
Lowest
High
Highest


Key Advantage
High-temp stability
Low cost
Highest energy density
Extreme temp stability




Selection Guidelines

Low Magnetic Strength, High Temperature: Choose Alnico (e.g., sensors, crafts).
Cost-Sensitive, General-Purpose: Opt for ferrite (e.g., consumer electronics, automotive).
Highest Magnetic Strength, Compact Size: Use NdFeB (e.g., EVs, wind turbines, robotics).
Extreme Temperature/Corrosion Resistance: Select SmCo (e.g., aerospace, military, medical).

This comparison highlights the trade-offs between magnetic performance, cost, and temperature resistance, enabling informed decisions across industries.