Editor's words: Surface roughness Ra is a symbol that we often use when working on machinery. It is basically an old friend of ours. Without it, the drawing would probably be useless. It is such a symbol that we deal with every day. You Do you know why 0.8, 1.6, 3.2, 6.3, 12.5 are used instead of other numbers? I believe that friends in the community have also had this confusion when learning and using it, but they have not studied the answer in detail. It all starts with great mathematics. Now let me tell you in detail.
Everything comes from the great priority number system!
French engineer Renault saw that the wire ropes on the hot air balloons had various specifications, so he thought of a way. He raised 10 to the fifth power and got a number of 1.6. Then he multiplied the numbers to get the following five priority numbers:
1.0
1.6
2.5
4.0
6.3
This is a geometric sequence, and the last number is 1.6 times the previous number. Then there are only 5 types of wire ropes below 10, and there are only 5 types of wire ropes from 10 to 100, namely 10, 16, 25, 40, and 63.
However, this division method was too sparse, so Mr. Lei continued his efforts and raised 10 to the 10th power, and obtained the R10 priority number system as follows:
1.0
1.25
1.6
2.0
2.5
3.15
4.0
5.0
6.3
8.0
The common ratio is 1.25, so there are only 10 types of steel wire ropes within 10, and there are only 10 types of wire ropes between 10 and 100, which is more reasonable. At this time, someone must have said that in this sequence, the first numbers seem to be not much different, such as 1.0 and 1.25. There is almost no difference. I usually round up, but the gap between 6.3 and 8.0 is large. Is this reasonable?
Reasonable or not, let's make an analogy. For example, the natural numbers 1, 2, 3, 4, 5, 6, 7, 8, 9 look very smooth. We use this sequence to pay wages, giving 1,000 to Zhang San and 2,000 to Li Si. Both of them are convinced. There is sudden inflation. Give Zhang San 8,000 and Li Si 9,000. In the past, Li Si's salary was twice that of Zhang San, but now it is 1.12 times. Do you think Li Si would be willing? He is the supervisor, and giving him 16,000 is not enough. Zhang San will not complain that the supervisor has 8,000 more than him.
There are two ways to compare things in nature, namely "relative" and "absolute"! The priority number system is relative.
Some people say that his product specifications are 10 tons, 20 tons, 30 tons, and 40 tons. Now it seems unreasonable, right? If you take double, it should be 10 tons, 20 tons, 40 tons, 80 tons, or keep the head and tail, it should also be 10 tons, 16 tons, 25 tons, 40 tons, the common ratio is 1.6.
This is "standardization". I often see people talking about "standardization" on forums. In fact, what they are talking about is "standard parts." What they do is just sort out the standard parts of the whole machine, which is called standardization. In fact, it is not like this. . For true standardization, you need to serialize all parameters of your product according to the priority number system, and then serialize the functional parameters and dimensions of all components using the priority number system.
Natural numbers are infinite, but in the eyes of mechanical designers, there are only 10 numbers in the world, which are the R10 priority numbers. Moreover, when these 10 numbers are multiplied, divided, raised, and squared, the result is still among these 10 numbers. How amazing! When you are designing and don't know what size to choose, just choose from these 10 numbers. How convenient it is!
1.0 N0
1.12 N2
1.25 N4
1.4 N6
1.6 N8
1.8 N10
2.0 N12
2.24 N14
2.5 N16
2.8 N18
3.15 N20
3.55 N22
4.0 N24
4.5 N26
5.0 N28
5.6 N30
6.3 N32
7.1 N34
8.0 N36
9.0 N38
Two priority numbers, such as 4 and 2, have serial numbers N24 and N12 respectively. When they are multiplied and their serial numbers are added, the result is equal to N36 or 8; when divided, the serial numbers are subtracted and the result is equal to N12 or 2. ; For the cube of 2, multiply its serial number N12 by 3 to get N36, which is 8; for the square root of 4, divide its serial number N24 by 2 to get N12, which is 2. What if we find the fourth power of 2? N12*4=N48, there is no one here, what should I do? In the above list, there is no previous number, which is 10. Its serial number is N40. If the serial number is greater than 40, only look at the part greater than 40. For example, for N48, look at N8, which is 1.6, and then multiply it by 10 to get 16. . If the serial number is N88, look at N8 to get 1.6, then multiply it by 100 to get 160, because the serial number of 100 is N80, the serial number of 1000 is N120, and so on for mechanical design, it is enough to use these 20 numbers for a lifetime. But sometimes it is necessary to use the R40 number system. It is more complete with 40 numbers. If it is not enough, there is also the R80 series. I know the R40 number system by heart and don't even need a calculator for general calculations. Simply put, calculate the torsion resistance of 40-diameter 45 steel. The torsion coefficient is 0.5*π*R^3. The torsional stress is half of the yield point of 360, which is 180MPa. The pi is 3.15. Use your left and right hands to pinch the decimal point and mentally calculate the addition and subtraction of serial numbers. Come out in a moment. Did anyone say you don't add a safety factor? Tell me, should I choose 1.25, 1.5, or 2? hehe.
The golden section is 0.618, which is 1.618, and there is also 1.6 here.
The square root sequence is square root 1, square root 2, square root 3. It's easy to find, right? (The serial number of 3 is N19)
What is π squared? equal to 10. Is it convenient when you calculate that the pressure rod is stable?
The torsion coefficient of a round rod is about 0.1*D^3. Now you can calculate the torsion coefficient verbally, right?
Why did the big screw jump directly from M36 to M40?
Why does the gear transmission ratio have 6.3 or 7.1?
Why does channel steel have a 12.6 gauge that is rarely seen on the market?
Why did the outsourcing factory call and say that there are no 140 square tubes, but there are 120 and 160? Because the R5 number system takes precedence over the R20 number system.
Why do the parameters of standard parts have a first sequence and a second sequence? Generally speaking, the first sequence is the R5 sequence.
Why does Inventor's screw hole list have M11.2? Now you know it's not a fabricated number, right?
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There are also steel plate thickness, section steel model, gear module, all standard parts, functional parameters, dimensional parameters, standard tolerance tables on all industrial product samples, etc., etc., their origins are slowly becoming clear in our hearts at this moment. . It can be said that we have understood half of the mechanical design manual, as well as those industrial products that have not yet been made.
Then, when we design a product, we can design a series at the same time, instead of carrying out the so-called "standardization" after the design is completed; further, if the product is destined to be serialized, then we can even design it according to the actual working conditions. Design the product without knowing much about it because the priority number system already includes all models.
The applications of the priority number system, listed above, can be described as a drop in the ocean, and there are endless applications waiting for us to develop ourselves.
Now that we understand the origin of the surface roughness value, let's take a look at the knowledge of surface roughness!
1. The concept of surface roughness
Surface roughness refers to the unevenness of the machined surface with small spacing and tiny peaks and valleys. The distance (wave distance) between the two wave crests or the two wave troughs is very small (less than 1mm), which is a microscopic geometric shape error.
Specifically refers to the height and spacing S of small peaks and valleys. Generally divided into S points:
S
1≤S≤10mm is waviness
S>10mm is f shape
2. VDI3400, Ra, Rmax comparison table
National standards stipulate that three indicators are commonly used to evaluate surface roughness (unit: μm): the average arithmetic deviation Ra of the profile, the average height of unevenness Rz, and the maximum height Ry. The Ra indicator is often used in actual production. The maximum microscopic height deviation Ry of the contour is commonly expressed by the Rmax symbol in Japan and other countries, and the VDI indicator is commonly used in Europe and the United States. The following is a comparison table of VDI3400, Ra and Rmax.
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VDI3400, Ra, Rmax comparison table
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3. Factors causing surface roughness
Surface roughness is generally caused by the machining method used and other factors, such as the friction between the tool and the part surface during the machining process, the plastic deformation of the surface metal during chip separation, and high-frequency vibration in the process system, electrical machining discharge pits, etc. Due to different processing methods and workpiece materials, the depth, density, shape and texture of the marks left on the processed surface are different.
4. The main effects of surface roughness on parts
Affect wear resistance. The rougher the surface, the smaller the effective contact area between mating surfaces, the greater the pressure, the greater the friction resistance, and the faster the wear.
Affects the stability of the fit. For clearance fits, the rougher the surface, the easier it is to wear, causing the gap to gradually increase during work; for interference fits, the actual effective interference is reduced due to the flattening of microscopic convex peaks during assembly. the connection strength.
Affects fatigue strength. There are large troughs on the surface of rough parts, which, like sharp corners and cracks, are sensitive to stress concentration, thus affecting the fatigue strength of the part.
Affects corrosion resistance. Rough parts surfaces can easily allow corrosive gases or liquids to penetrate into the inner metal layer through microscopic valleys on the surface, causing surface corrosion.
Affect sealing. Rough surfaces cannot fit tightly together, and gas or liquid leaks through the gaps between the contact surfaces.
Affects contact stiffness. Contact stiffness is the ability of the joint surface of parts to resist contact deformation under the action of external forces. The stiffness of a machine depends largely on the stiffness of the contact between the various parts.
affect the measurement accuracy. The surface roughness of the measured surface of the part and the measuring surface of the measuring tool will directly affect the accuracy of the measurement, especially in precision measurement.
In addition, surface roughness will have varying degrees of impact on the parts' coating, thermal conductivity and contact resistance, reflective ability and radiation performance, resistance to liquid and gas flow, and conductor surface current flow.
5. Basis for surface roughness evaluation
1. Sampling length
The sampling length L is the length of a reference line specified for evaluating surface roughness. The length that can reflect the surface roughness characteristics should be selected based on the actual surface formation and texture characteristics of the part. The sampling length should be measured based on the general direction of the actual surface profile. The sampling length is specified and selected in order to limit and reduce the effects of surface waviness and shape errors on the surface roughness measurement results. Commonly used options for roughness meters are: 0.25mm, 0.8mm, 2.5mm
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2. Assessment length
The evaluation length is a length necessary to evaluate the profile, which may include one or several sampling lengths. Since the surface roughness of various parts of the part surface is not necessarily uniform, one sampling length often cannot reasonably reflect a certain surface roughness feature. Therefore, several sampling lengths need to be taken on the surface to evaluate the surface roughness. The evaluation length generally includes 1 to 5 sampling lengths L. When the sampling length is 0.8 and the evaluation length is 5L, 5X0.8=4mm
3. Baseline
The reference line is the contour center line used to evaluate surface roughness parameters. There are two types of baselines: the least squares midline of the contour: within the sampling length, the sum of squares of the contour offsets of each point on the contour line is the smallest, and it has a geometric contour shape. Arithmetic mean center line of the contour: Within the sampling length, the areas of the contours on both sides of the center line are equal. Theoretically, the least squares center line is the ideal baseline, but it is difficult to obtain in practical applications. Therefore, the arithmetic mean center line of the contour is generally used instead, and a straight line with an approximate position can be used instead during measurement.
4. Measuring stroke
The measurement stroke refers to the moving distance of the sensor stylus on the actual workpiece. The measurement stroke is usually the calculation relationship of the evaluation length plus 2 sampling lengths: for example, when the evaluation length is selected as 5L, the sampling length L is 0.8mm, the measurement stroke is 5L+2L=7L, and the measurement stroke is 7X0.8=5.6mm. Know this Very important, the distance traveled on the workpiece can be calculated. This determines the contact surface size of the smallest workpiece measured by the user.
6. Surface roughness evaluation parameters
1. Height characteristic parameters
Ra arithmetic mean deviation of the contour: the arithmetic mean of the excellent values of the contour deviation within the sampling length (lr). In actual measurement, the greater the number of measurement points, the more accurate Ra is.
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Rz Maximum profile height: The distance between the peak line and the bottom line of the valley.
Ra is preferred within the commonly used range of amplitude parameters. Before 2006, there was another evaluation parameter in the national standard: "The ten-point height of microscopic unevenness", which is represented by Rz, and the maximum height of the contour is represented by Ry. After 2006, the ten-point height of microscopic unevenness was canceled in the national standard, and was adopted. Rz represents the maximum height of the profile.
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2. Spacing characteristic parameters
Rsm Average width of contour cells. The average spacing of microscopic irregularities in the profile within the sampling length. The micro-irregularity spacing refers to the length of the contour peak and the adjacent contour valley on the center line. For the same Ra value, the Rsm value is not necessarily the same, so the reflected texture will be different. Surfaces that value texture usually focus on the two indicators of Ra and Rsm.
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The Rmr shape characteristic parameter is expressed by the profile support length ratio, which is the ratio of the profile support length to the sampling length. The contour support length is the sum of the lengths of the sections obtained by intersecting the contour with a straight line parallel to the center line and distance c from the contour peak line within the sampling length.
7. Surface roughness measurement method
1. Comparative method
Used for on-site measurements in workshops, often used for measurements on medium or rough surfaces. The method is to determine the roughness value of the measured surface by comparing it with a roughness sample marked with a certain value.
2. Stylus method
Surface roughness uses a diamond stylus with a tip radius of curvature of about 2 microns to slowly slide along the measured surface. The up and down displacement of the diamond stylus is converted into an electrical signal by an electrical length sensor. After amplification, filtering and calculation, it is indicated by a display instrument. To obtain the surface roughness value, a recorder can also be used to record the profile curve of the measured section. Generally, measuring tools that can only display surface roughness values are called surface roughness measuring instruments, while those that can record surface profile curves are called surface roughness profile meters. Both measuring tools have electronic calculation circuits or computers, which can automatically calculate the arithmetic mean deviation of the profile Ra, the ten-point height of micro-irregularity Rz, the maximum height of the profile Ry and other various evaluation parameters. They have high measurement efficiency and are applicable For measuring surface roughness Ra of 0.025 ~ 6.3 microns.
3. Light sectioning method
The light strip formed after the light passes through the slit is projected onto the measured surface, and the surface roughness is measured based on the contour curve formed by its intersection with the measured surface (Figure 3). After the light emitted from the light source passes through the condenser, slit, and objective lens 1, the slit is projected onto the measured surface at an inclination angle of 45° to form a cross-sectional profile figure of the measured surface, which is then amplified and projected onto the measured surface through objective lens 2. on the reticle. Use the micrometer eyepiece and reading drum to first read the h value, and then calculate the H value.
