Definition and performance of spring steel

Spring steel refers to steel specially used to manufacture springs and elastic elements due to its elasticity in the quenched and tempered state. The elasticity of steel depends on its ability to deform elastically, that is, the ability to deform elastically within a specified range Make it bear a certain load, and there will be no permanent deformation after the load is removed.

Spring steel should have excellent comprehensive properties, such as mechanical properties (especially elastic limit, strength limit, yield ratio), elastic reduction performance (that is, elastic reduction resistance, also known as relaxation resistance), fatigue performance, hardenability , Physical and chemical properties (heat resistance, low temperature resistance, oxidation resistance, corrosion resistance, etc.). In order to meet the above performance requirements, spring steel has excellent metallurgical quality (high purity and uniformity) and good surface quality (strict surface control) Defects and decarburization), precise shape and size.

According to the “Steel Classification” standard, according to the basic performance and use characteristics, spring steel belongs to mechanical structural steel; according to the quality level, it belongs to special quality steel, that is, steel that requires strict quality and performance control during the production process. According to China’s custom , Spring steel belongs to special steel.

Correction process of classification spring

After the end face grinding of the spiral compression spring is completed, if the free height, perpendicularity, pitch, and outer diameter of the spring does not reach the deviation specified on the drawing, it is often necessary to correct the processing.

The calibration operation is currently in manual or semi-manual operation. Commonly used tools are: springs with a wire of 4mm or more, mostly hand-pull presses, splitters, punches, etc.; springs with a wire of 4mm or less are mostly used. Special tools, pliers, hammers, etc. for wedge-shaped blades. Correction processing is to use these tools to locally deform the spring to achieve the size required by the drawing.

1. Application of calibration process

1.1 Correction of outer diameter. In general, the coil spring can guarantee the deviation of the outer diameter, but when the winding ratio of the spring is too large and the spring outer diameter tolerance requirements are particularly strict (exceeding the requirements of the relevant spring standards), the outer diameter needs certain correction .

The commonly used correction tools are special pliers, special pressure plates and spindles.

1.2 Pitch and height correction. When the pitch is used as the main acceptance index and the free height of the spring cannot be guaranteed, the correction method can be used to adjust.

1.3 Verticality correction. In order to meet the requirements of high-precision verticality, and when grinding cannot be guaranteed, correction can be used to improve the accuracy of verticality.

2. Pros and cons of correction

The correction process is to use a certain tool to cause the spring to produce local plastic deformation to meet the requirements specified on the drawing. The correction has two sides: on the one hand, it improves the dimensional accuracy, and on the other hand, it often causes adverse effects on the performance of the spring, and even brings damage.

In order to reduce the influence of correction on spring performance, stress relief annealing treatment should be carried out after correction.

3. Ways to reduce correction

The calibration is labor-intensive, time-consuming, and increased manufacturing costs. Therefore, measures should be taken from the following aspects to reduce or eliminate the calibration process.

3.1 Under the premise of ensuring the main performance of the spring, try not to set too high requirements for the verticality, pitch uniformity and other indicators during the design.

3.2 Improve the uniformity and stability of the mechanical properties of spring materials, especially the fluctuation range of the tensile strength of spring materials should be as small as possible.

3.3 Improve the precision of coil springs. Make the helix angle, lap and pitch of both ends of the spring uniform, and the free height error is controlled within a certain range.

3.4 Improve the precision of the grinding spring. Make the verticality of the spring meet the requirements of the drawing as much as possible.

Current status of spring steel production technology at home and abroad

Understand the current situation of spring steel production processes at home and abroad:

Pure steel smelting, alloying and microalloying, and controlled rolling and cooling technology support the development of domestic spring steel, but the two key indicators of surface defects and decarburization of domestic spring steel are difficult to reach the level of similar foreign products, and comparative research is needed. The comparison production process is as follows:

A. Domestic Baosteel

The production process is: scrap steel + molten iron-150t electric furnace-refining-continuous casting-billet surface peeling-heating-high-speed wire rolling-Stermore cooling-inspection and delivery; in addition, the process is blast furnace ironmaking –Pretreatment of molten iron – converter steelmaking – secondary refining – die casting – blooming – billet finishing – wire rod rolling – inspection and delivery.

Features: Strengthen the refining operation, adopt electromagnetic stirring of the crystallizer, improve the deoxidation process, and control the rolling. The spring wire has pure steel, small segregation, shallow decarburization, and good surface quality. Dongguan Spring

B. Shagang Huaigang

Shagang Group’s Huaigang production springs are typical and representative.

The process flow is: electric furnace/100t converter-refining furnace (LF, RH)-continuous casting-billet heating-bar and profile continuous rolling production.

Process characteristics: In addition to the use of electromagnetic stirring in the mold to strengthen the secondary refining, the deoxidation process and the continuous casting speed adjustment should be introduced to continuously reduce the superheat of the tundish under the premise of ensuring the purity of the molten steel, and greatly improve the quality of continuous casting. .

C. Kobe Steel Corporation, Japan

Japan’s Kobe Steel Company adopts surface modification technology, nitriding treatment and surface shot peening technology of spring steel wire for valves to improve the strength of valve springs.

The process flow is: billet-hot rolling-deburring-lead bath quenching-drawing-oil quenching-tempering-eddy current testing-cold coil-stress relief-coil end grinding- Nitriding treatment-shot peening treatment-stress aging-storage.

It is known that most of the suspension springs and valve springs used by well-known high-end brands at home and abroad are produced by wire rods or bar round steel from Japan’s Kobe Steel Company.

D. Nangang

Process flow: 100t UHP electric furnace-LF-VD vacuum furnace-five-machine five-strand continuous casting-cooling-heating furnace-rolling-cooling-cut to length-packaged and put into storage.

Process characteristics: The electric furnace in the smelting adopts a large carbon content, a low-aluminum clean steel process and a high-basicity slag, vacuum degassing, and protective casting. The calcium metamorphism technology is used to reduce the size of non-metallic inclusions. The online top forging test is used to prevent Surface defects.

Recently, Nanjing Iron & Steel has made a big breakthrough in the development of high-speed spring steel series wire rods, and its ф13mm38Si7 high-speed spring steel base material has been exported to Germany.

Application analysis of new technology of surface treatment of mould spring

Application analysis of new technology for mold spring surface treatment:

Existing molds are the main process equipment for industrial production. The development of modern industrial products and the improvement of technical levels largely depend on the development level of the mold industry. Since the Second World War, the increase in automation has led to the rapid development of foreign molds Although China is a big country in mold production, it is not a strong country in mold manufacturing. For springs that match the mold, this detail is also the key to achieving quality. It affects the performance of the entire mold. Industrial springs

Performance analysis: A good paint layer to match the surface treatment of the spring can be described as killing two birds with one stone. The color is used to identify various technical parameters, which is convenient for industrial production operations, and the anti-corrosion performance of the spring surface can be better guaranteed.

The surface of the spring is identified by various paint layers. For example, light and small loads are represented by yellow paint; light loads are represented by blue paint; medium loads are represented by red paint; extremely heavy loads are represented by brown paint;

At present, the main manufacturers that successfully use the above methods are many foreign manufacturers, such as Japan Tohatsu Corporation.

Electrophoretic paint is used in foreign countries. In a water-soluble paint tank, the workpiece is used as a cathode, and a certain voltage and time are applied to form a uniform thickness of paint on all surfaces of the spring, and then it can be cleaned and dried. Clean and bright, no particles, no bottoming phenomenon, good binding force, not easy to fall off, good hardness of 3-4H, if the British LVH company polyurethane cathodic electrophoretic paint is used, its flexibility is quite good. The operating environment has no strong solvent smell, and the air There is little pollution, and the wastewater treatment and discharge process is simple, as long as the resin of the PH sedimentation electrophoretic paint is adjusted, and then the clear water is discharged.

In China, only a small number of manufacturers have effectively visited. At present, it is mainly due to some fixed technical requirements, such as the use of imported materials to reach foreign levels, but there is an obvious gap in the surface treatment effect of the entire spring.

Generally, manual painting is used in China, and the appearance will appear sagging, leaking, poor combination, and poor rust resistance. The limitations of its own process cause a large number of products to be stripped and reworked.

The characteristics and design principles of toy springs

The characteristics and design principles of toy springs:

With the development of the mold industry, the number and varieties of special-shaped section steel wire mold springs are increasing. Special-shaped section mold springs have the characteristics of large stiffness, long life, and small size. However, the development of its design theory has been relatively slow. At present, except for square sections In addition to the more mature design methods of strong springs, the design methods of other cross-section strong springs are basically based on the specific cross-section through the test, find the correction coefficient to obtain the empirical design formula of the specific cross-section, and now give a brief introduction to the characteristics and design problems of this type of spring .

In the same space, the load-bearing capacity of the square section wire spring is 43-48% higher than that of the round section spring. Obviously, the rectangular spring is more than 50%.

From the analysis that excessive stress is the main reason for spring failure, under the same conditions, the service life of the special-shaped section wire spring is 13-14% longer than that of the round section wire spring.

Special-shaped cross-section wire spring can produce large deformation.

Special-shaped wire springs are heavy. Spring manufacturers

The linearity is better than that of the circular section spring, that is, the stiffness tends to be more constant. Especially the spring with the long side parallel to the axis.

The scope of application is subject to certain restrictions: from the analysis, it can be seen that if the special-shaped cross-section material spring cannot fully use its advantages, it will not produce economic benefits. Under what circumstances should it be used?

(1) The design load cannot be achieved with round cross-section materials.

(2) Replace the circular cross-section compound spring.

(3) When the round material spring cannot reach the required deformation.

(4) Where the spring installation space is small.

(5) Where strict spring characteristics are required.

《一》Mold spring design principles

A. The choice of spring material allowable stress [τ] should be mainly considered to ensure the fatigue life of the spring. The dynamic life of the spring is generally divided into three categories:

Class I: The number of alternating loads is 106; Class II: The number of alternating loads is 10?-105; Class III: The number of alternating loads is less than 10?;

B. When designing non-rectangular shaped cross-section springs, it is necessary to derive and draw curves or calculation formulas in different rotation ratios, different width to thickness ratios, deformation correction coefficients (τ) and shear stress correction coefficients (β).

C. The material width-to-thickness ratio (a/b) should not be too large, and the winding of the spring should not be too small.

D. According to the given conditions and constraints, choose a design method that is simple to calculate and select reasonable parameters.

The remaining problems in “Two”

A. The low degree of standardization of mold design limits the development speed of standardized mold springs.

B. The design theory is not perfect. At present, the rectangular cross-section spiral spring is more mature, but its tolerance selection is still inconclusive. The special-shaped cross-section spiral spring is based on the rectangular cross-section, which has been corrected by experiment.

C. The degree of standardization of mold springs is low. At present, there is no official national standard or industry standard in China except for the QC7111-7113 standard formulated by our institute for the automotive industry. Mold designers have no standard to choose from is an urgent problem to be solved.

d. There are no designated factories for the production of special-shaped cross-section materials, especially oil-quenched and tempered steel wire suppliers that do not have such materials. The materials restructured by the spring manufacturers themselves are of unstable quality and high cost, which affects the promotion and application of such springs .

E. There is no special coil spring equipment for the production of such springs. The coil spring winding ratio for molds is generally less than 4, while the domestic coil spring machine is suitable for springs with a winding ratio above 4.

Introduction to the development direction of the spring industry market

Spring industry market development:

Daily hardware market demand is strong

The daily necessities industry and the hardware industry, including lighters, toys, locks, door hinges, fitness equipment, mattresses, sofas, etc., have the largest demand for springs in terms of quantity, tens of billions, and the technical requirements are not high, and the price is very high. Low, generally produced by small spring factories scattered across the country, they have unique advantages in cost, and it is difficult for large spring factories to compete with them. In recent years, the domestic market has a strong demand for daily hardware products, which has driven the growth of supporting springs Therefore, new spring companies are born from time to time. In the future, market demand will grow at a rate of 7% to 10% per year. After China’s entry into the WTO, the export volume of daily hardware products has increased significantly, and the demand for springs will be driven by the international market. The impact of market demand and trade barriers, the international market has its uncertain side.

Although the spring is small, as a general-purpose basic component, it has a large quantity and a wide range of varieties, and its application fields involve almost all fields of the national economy, making a huge contribution. In recent years, the rapid development of China’s national economy has also driven the rapid growth of China’s spring industry. Experts predict that this growth trend will continue, and the industry-wide sales will exceed 4 billion yuan by 2010. According to analysis, there are currently five major markets for spring products: transportation, daily hardware, instrumentation and Electronic appliances, industrial and mining accessories, overseas export markets.

The transportation market has the strongest driving force

The transportation market, including the provision of supporting and maintenance parts springs to industries such as automobiles, motorcycles, diesel engines and railways, is the most important and promising market in the spring industry at present, with sales close to 40% of the entire industry, and only the automotive industry In 2002, the demand for suspension springs was 7 million pieces, 100 million pieces of valve springs (including motorcycle and diesel engine manufacturing), and 1.2 million stabilizers. In 2002, the total sales of springs for supporting and providing maintenance parts for these industries exceeded 1 billion yuan. .

In the next 5-7 years, China’s automobile industry will enter a stage of rapid growth, with an annual growth rate of 15% to 25%. In 2003, the demand for suspension springs is expected to be close to 10 million, and the demand for stabilizers is 1.6 million. The rapid development of the industry has had an obvious pulling effect on the spring industry. It has become the largest user of the spring industry and has attracted the attention of foreign spring counterparts. In addition to a few foreign capital and joint ventures that have entered the Chinese market first, the Japanese Clockwork Co., Ltd. The club and the Central Spring Co., Ltd. have also entered China and must have a place in this market.

There is also a major potential market in the spring industry is the railway system. With the deepening of the reform of the railway system, the gradual opening of the market and the implementation of the high-speed railway plan, the vehicle shock absorption system is facing upgrades, and the railway line needs to install new shock and noise reduction Components, will bring huge business opportunities to the spring industry. Some companies have been listed as the designated units of high-speed train springs by the Ministry of Railways, and some units are developing rubber-metal composite springs for vibration and noise reduction of high-speed railway tracks. The market of the system has just begun to open to the external system, although the degree of openness is not large, the potential is considerable.

In the next few years, the motorcycle industry will not have much growth, and will still maintain the current annual output of 13 million units. The demand for motorcycle shock absorber springs and clutch springs will remain at the level of 50 million and 40 million. The increase in requirements, the decrease in the proportion of two-stroke motorcycles, and the increase in the proportion of four-stroke motorcycles, will bring a certain increase to the valve spring.

What is the spring national standard

State the spring national standard:

China’s spring standardization work began in the early 1960s and has been more than 40 years old. A relatively complete standard system has been formed. Currently, there are 22 spring national standards and 30 industry standards. In 1999, the National Quality Supervision Administration approved the establishment of the country Spring Standardization Technical Committee (SAC/TC235), spring standardization work has been fully promoted. In 2004, ISO/TC 227 (spring) was established internationally, and China participated in the work as a member, which marked that China’s spring standardization work has entered a new stage , That is; comprehensive tracking and substantial participation in the work phase.

GB/T 1239.2-1989 Cold rolled cylindrical spiral compression spring technical conditions

GB/T 1239.3-1989 Cold rolled cylindrical spiral torsion spring technical conditions

GB/T 1239.4-1989 Technical requirements for hot-rolled cylindrical spiral spring

GB/T 1239.6-1989 Cylindrical spiral spring design calculation

GB/T 1973.1-1989 small cylindrical spiral spring technical conditions

GB/T 1973.2-1989 Small cylindrical spiral tension spring Dimensions and parameters

GB/T 1973.3-1989 small cylindrical spiral compression spring dimensions and parameters

GB/T 2087-2001 Cylindrical spiral stretch bullet size and parameters (half-circle hook and loop type)

GB/T 2088-1997 Cylindrical spiral stretch bullet (round hook and ring pressure center type) dimensions and parameters

GB/T 2089-1994 cylindrical spiral compression spring (the two ends are grounded flat or forged flat) size and parameters

GB/T 4142-2001 Cylindrical spiral stretch bullet size and parameters (round hook and loop type)

GB/T 2785-1988 Technical requirements for internal combustion engine valve springs

GB/T 2940-1982 Technical requirements for fuel injection pumps, governors and injector springs for diesel engines

GB/T 4036-1983 watch spring

GB/T 4037-1983 watch hairspring

GB/T 1972-2005 Disc spring

GB/T 10867-1989 spring shock absorber

GB/T 13828-1992 multi-strand cylindrical coil spring

GB/T 9296-1988 floor spring

GB/T 1805-2001 spring term

GB/T 1358-1993 cylindrical spiral spring size series

JB/T 6655-1993 high temperature resistant spring technical conditions

JB/T 10416-2004 helical spring for automobile suspension technical conditions

JB/T 10417-2004 Motorcycle shock absorber spring technical conditions

JB/T 10418-2004 Gas spring design calculation

JB/T 6653-1993 flat steel wire cylindrical spiral compression spring

JB/T 6654-1993 plane scroll spring technical conditions

JB/T 7366-1994 Plane scroll spring design calculation

JB/T 8584-1997 rubber-metal spiral composite spring

JB/T 9129-2000 60Si2Mn steel spiral spring metallographic inspection

JB/T 9127-2000 Cylindrical spiral spring shot peening technical specifications

JB/T 3338.1-1993 hydraulic parts cylindrical spiral compression spring technical conditions

JB/T 3338.2-1993 hydraulic cylinder spiral compression spring design calculation

JB/T 8046.1-1996 compressed gas spring

JB/T 8046.2-1996 lockable gas spring

JB/T 7367.1-2000 Cylindrical spiral compression spring ultrasonic flaw detection method

JB/T 7757.1-1995 Cylindrical spiral spring for mechanical seal

JB/T 7283-1994 Technical requirements for leaf springs for agricultural machinery

JB/T 50022-1994 Agricultural machinery leaf spring product quality classification

JB/T 3383-1983 Test method for automobile leaf spring bench

JB/T 3782-1984 Metallographic Inspection Standard for Automobile Leaf Springs

JB/T 539-1984 Automotive leaf spring pin and lug technical conditions

ZB T 06001-1988 Specification for shot peening of automobile leaf spring

QCn29035-1991 Technical requirements for automobile leaf springs

QC/T 29103-1992 Quality grading regulations for automobile leaf springs

JB/T 53394-2000 Disc spring product quality classification

JB/T 3396-2000 Cylindrical spiral compression spring for hydraulic parts Product quality classification

JB/T 58700-2000 Spring Product Quality Classification General Rules

JB/T 58701-2000 Small cylindrical coil spring Product quality classification

JB/T 58702-2000 Cylindrical spiral spring Product quality classification

JB/T 7944-2000 Cylindrical spiral spring sampling inspection

National Standard for Disc Spring

The national standard of disc spring and its application principle:

Disc spring national standard GB/T1972-92

The disc spring standard specifies the size series, technical requirements, test methods, inspection rules and design calculations of disc springs

The disc spring standard applies to general disc springs

The disc spring standard does not apply to trapezoidal section disc springs, slotted disc springs and wax disc springs

Disc spring reference standard:

GB /T 1222 spring steel

GB/T 2828.1 Sampling inspection procedure by attributes Part 1: Batch inspection sampling plan retrieved by acceptance quality limit (AQI.)

(GB/T 2828.1-2003, ISO 2859-1:1999, IDT)

GB /T 3 279 spring steel hot rolled sheet

GB/T 4 340.1 Metal Vickers Hardness Test Part 1: Test Method (GB/T 4340.1-1999, egvI SO 6507-1:1997)

YB /T 5058 Spring steel, tool steel cold rolled steel strip


The disc spring is a special spring that is tapered in the axial direction and bears the load. After the load is deformed, a certain potential energy is stored. When the bolt is loosened, the disc spring releases part of the potential energy to maintain the pressure between the flange connections. Sealing requirements. The stress distribution of the disc spring decreases evenly from the inside to the outside, which can achieve the effect of low stroke and high compensation force.


In a large range, disc springs are replacing cylindrical spiral springs. They are often used in heavy machinery (such as presses), artillery, aircraft and other weapons, as powerful buffers and damping springs, and used as clutches and safety valves for vehicles and tractors. The compression spring and the energy storage element used as a motorized device.

Disadvantages: The load deviation is difficult to guarantee.

Disc springs can be divided into three categories according to the different cross-sectional shapes: including ordinary disc springs (the cross-sectional shape is rectangular), disc springs with radial grooves, and trapezoidal cross-section disc springs. Common disc springs are divided into: There are two types of support surface and unsupported surface; the disc spring with radial grooves is based on ordinary disc springs, and several uniformly distributed grooves are opened in the radial direction. The grooves can be opened from the inner hole to the outer circle. It can also be opened from the outer circle to the inner control direction; the trapezoidal cross-section disc spring can be divided into two types: the inner edge thickness is greater than the thickness of the external aid and the inner edge thickness is less than the thickness of the outer circle. Due to the deformation of the single-piece disc spring and The load value often cannot meet the requirements of use. At this time, it can be used in groups to form a disc spring assembly (column). The typical combination method is: stack combination disc spring, composite combination disc spring and other combination disc springs.

Compared with cylindrical coil springs, disc springs have the following characteristics:

A, the load deformation characteristic curve is nonlinear.

B, the disc spring is in the shape of a thin plate, which is easy to form a composite part, and can be assembled and replaced in a modular manner, thus bringing convenience to maintenance.

C, the disc spring with radial groove has the characteristic of zero stiffness. This characteristic can be used in a certain deformation range where the spring force is basically stable.

D. The vibration absorption performance of the disc spring is not lower than that of the cylindrical coil spring. When the laminated combination is used, the friction between the disc springs will have greater damping and dissipate impact energy.

Spring design_material development

Development of spring processing technology, design and materials:

Automobile springs are mainly developed in the direction of high strength to reduce quality; electronic product springs are mainly developed in the direction of smaller shape; and optical device springs are mainly developed in the direction of both high strength and small shape. Corresponding spring design methods, materials and There have been developments in processing technology and other aspects.

In electromechanical products, there are three main types of springs with the largest amount:

A) Motor vehicle springs based on automobiles;

B) Electronic product springs based on household appliances;

C) Optical device springs mainly for video cameras, copiers and cameras.

One, the development of spring design

At present, the widely used spring stress and deformation calculation formulas are derived based on material mechanics. Without certain practical experience, it is difficult to design and manufacture high-precision springs. With the increase of design stress, many previous experiences are not Reapplicable. For example, after the design stress of the spring is increased, the helix angle increases, which will cause the fatigue source of the spring to be transferred from the inner side of the coil to the outer side. For this reason, sophisticated analytical techniques must be used, and the current widely used methods are limited Meta method (FEM).

The characteristics of vehicle suspension springs are that in addition to sufficient fatigue life, their permanent deformation must be small, that is, the relaxation resistance must be within the specified range, otherwise the center of gravity of the vehicle body will be shifted. At the same time, environmental corrosion must be considered for its fatigue life Impact. With the increase of vehicle maintenance period, more stringent requirements are put forward for permanent deformation and fatigue life. For this reason, high-precision design methods must be adopted. The finite element method can predict in detail the effect of spring stress on fatigue life and permanent deformation. The influence can accurately reflect the relationship between the material’s fatigue life and permanent deformation of the spring.

In recent years, the finite element method design method of spring has entered the practical stage, and there have been many reports of practical value, such as the effect of helix angle on spring stress; the relationship between stress and fatigue life calculated by finite element method, etc.

In addition, optimization design has been introduced in the design process of the spring. The structure of the spring is relatively simple, the function is simple, and the parameters that affect the structure and performance are saved. Therefore, the designer has long used analytical methods, graphic methods or graphic analysis methods to find the best The optimal design scheme has achieved certain results. With the development of computing technology, the use of computers to optimize the design of nonlinear programming has achieved results.

Reliability design is a series of analysis and design techniques adopted to ensure the reliability of the designed product. Its task is to make the designed product reach the specified reliability target on the basis of predicting and preventing the possible failure of the product. Value. It is a supplement and improvement to the traditional design method. Spring design has made certain progress in the use of reliability technology, but further improvement requires the development and accumulation of data.

With the development of spring application technology, designers have also put forward many new problems that need to be paid attention to and solved. For example, the influence of materials, strong pressure and shot peening on fatigue performance and relaxation performance is difficult to calculate accurately during design; it depends on experimental data. To determine; another example is the number of turns calculated according to the current design formula, the stiffness of the made spring is smaller than the design stiffness value, and the effective number of turns needs to be reduced to meet the design requirements.

The relationship between spring extension and tension

Talking about the relationship between spring elongation and pulling force

Studying the elongation of the spring: the elongation of the spring is related to the weight of the object hanging by the spring dynamometer, and the length of the spring is related to the hanging object. A spring dynamometer is used to hang a heavy object and a spring does not hang a heavy object. The length is different, and it is in a free state without hanging heavy objects.

The spring will stretch after hanging an object. The relationship between the length of a spring (cm) and the weight (kg) of the hanging object is known as the following table:

(1) The above table reflects the relationship between which variables, which is the independent variable and which is the dependent variable?

(2) When the weight of the object is 2kg, how does the length of the spring change?

(3) When the weight of an object gradually increases, how does the length of the spring change?

(4) If the weight of the object is xkg and the length of the spring is ycm, write the relationship between y and x according to the above table;

(5) When the weight of the object is 2.5kg, according to the relationship, there is no legend of heroes in the middle to find the length of the spring.

(1) Because the data in the table mainly relates to the length of the spring and the weight of the hanging object, it reflects the relationship between the mass of the hanging object and the length of the spring. The quality of the hanging object is the independent variable; the length of the spring Is the dependent variable;

(2) It can be seen from the table that when the mass of the object is 2kg, the length of the tension spring is 13cm;

(3) According to the data in the table, the length of the spring increases with the weight of the hanging object;

(4) According to the data in the table, when x=0, y=12, and every additional kilogram of weight increases the length by 0.5cm, so y=0.5x+12;

(5) Let x=2.5, substitute in the analytic formula of the function, and it can be solved. Spring manufacturer

Solution: (1) It reflects the relationship between the mass of Foshan ceramics and the length of the spring. The mass of the object is the independent variable; the length of the spring is the dependent variable;

(2) When the mass of the object is 2kg, the length of the spring is 13cm;

(3) When the mass of the object gradually increases, the length of the spring increases;

(4) According to the above table, the relationship between y and x is: y=12+0.5x;

(5) When x=2.5, y=12+0.5×2.5=13.75cm