Everything comes from the great priority number system!
The French engineer Renault saw that there are many specifications of the wire rope on the hot air balloon, so he thought of a way to open 10 to the 5th power to get a number 1.6, and then multiply the number to get 5 priority numbers as follows:
1.0
1.6
This is a geometric sequence, the last number is 1.6 times the previous number, then there are only 5 types of steel ropes below 10, and there are only 5 types of steel ropes from 10 to 100, namely 10, 16, 25, 40, 63.
However, this division method is too sparse, and Mr. Lei will continue to work hard and divide 10 to the power of 10 to get the R10 priority number system as follows:
The common ratio is 1.25, so there are only 10 kinds of wire ropes within 10, and there are only 10 kinds of wire ropes from 10 to 100, which is more reasonable. At this time, someone must say that the front numbers of this series seem to be similar, such as 1.0 and 1.25, there is almost no difference. I usually round off, but the interval between 6.3 and 8.0 is large. Is this reasonable?
Reasonable and unreasonable, let’s make an analogy. For example, the natural numbers 1, 2, 3, 4, 5, 6, 7, 8, and 9 seem to be very smooth. We use this sequence to pay wages. We send 1000 to Zhang San and 2000 to Li Si. Both are convinced. Suddenly inflation, 8000 was issued to Zhang San and 9000 to Li Si. In the past, Li Si’s salary was twice that of Zhang San, but now it has become 1.12 times. Do you think Li Si can be willing? He is the supervisor. Sending him 16,000 is almost the same. Zhang San will not complain that the supervisor has 8,000 more than him.
There are two ways to compare things in nature: “relative” and “absolute”! The priority number system is relative.
People say that his product specifications are 10 tons, 20 tons, 30 tons, and 40 tons. Now it seems unreasonable, right? If you take twice, it should be 10 tons, 20 tons, 40 tons, 80 tons, or keep the head and tail, it should be 10 tons, 16 tons, 25 tons, 40 tons, and the ratio of 1.6 is reasonable.
This is “standardization”. I often see people on the forums saying “standardization”, but in fact they are talking about “standard parts”. What they do is to sort out the standard parts of the whole machine, which is called standardization. Actually, this is not the case. . For true standardization, you have to serialize all the parameters of your product according to the priority number system, and then serialize the function parameters and dimensions of all parts 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 is the R10 priority number. Moreover, multiplying, dividing, exposing, and extracting these 10 numbers, the result is still in these 10 numbers, how amazing! When you design, when you don’t know what size you should choose, just choose from these 10 numbers. How convenient is it?
Two priority numbers, such as 4 and 2, whose serial numbers are N24 and N12 respectively, multiply them and add their serial numbers together, and the result is equal to N36, which is 8; divide and subtract serial numbers, which is equal to N12, which is 2 ; 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 here, what should I do? In the above list, there is no number written in it, which is 10, and its serial number is N40. If the serial number is greater than 40, only look at the part greater than 40. For example, N48 looks at N8, which is 1.6, and then multiplies by 10 to get 16. . Please pay attention to our WeChat ID: auto1950. If the serial number is N88, look at N8 to get 1.6, and then multiply it by 100 to get 160, because the serial number of 100 is N80, and 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 you need to use the R40 number series, there are 40 numbers, it is more complete, if not enough, there is also the R80 series. I have memorized the R40 number system backwards, and I don’t need a calculator for general calculations. In simple terms, the torsion resistance of 45 steel with 40 diameters is calculated. The torsion coefficient is 0.5*π*R^3. The torsion stress is half of the yield point 360, which is 180MPa. The pi ratio is 3.15. Come out in a while. Some people say you don’t add safety factor? Let’s just say, is it 1.25, 1.5, or 2? Ha ha.
The golden ratio is 0.618, which is 1.618. There is also 1.6 here.
The square root sequence is the root number 1, the root number 2, and the root number 3. Is it easy to find? (The serial number of 3 is N19)
What is the square of π? Equal to 10. Is it convenient when you calculate the pressure bar to be stable?
The torsion coefficient of the round rod is about 0.1*D^3, now you can calculate the torsion coefficient verbally?
Why does the big screw jump directly from M36 to M40?
Why is the gear ratio of 6.3 or 7.1?
Why does channel steel have a No. 12.6 which is rare in the market?
Why does the outsourcing factory call to say that there is no 140 square tube, but there are 120 and 160? Because the R5 number system has priority over the R20 number system.
Why does the parameter of the standard part 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 an M11.2? Now you know it’s not the number from Hu Die, right?
There are also steel plate thickness, section steel model, gear modulus, all standard parts, functional parameters on all industrial product samples, size parameters, standard tolerance tables, etc., and their sources are slowly becoming clear in our minds. . It can be said that we have understood half of the mechanical design manual and those industrial products that have not yet been made.
Then, when we are designing a product, we can design a series of products at the same time, instead of the so-called “standardization” after the design is completed; furthermore, if the product is destined to be serialized, then we can even compare the actual working conditions Design products without knowing it well, because all models have been included in the priority number system.
The applications of the priority number system, listed above, are a drop in the ocean, and endless applications are waiting for us to develop ourselves.
Understand the origin of the surface roughness value, let us take a look at the knowledge of surface roughness!
1. The concept of surface roughness
Surface roughness refers to the small spacing and small peaks and valleys of the processed surface. The distance (wave distance) between its two crests or two troughs is very small (below 1mm), which is a microscopic geometric shape error.
Specifically, it refers to the level of the tiny peaks and valleys Z and the distance S. Generally divided by S:
1≤S≤10mm is the waviness
S>10mm is f shape
2. Comparison table of VDI3400, Ra, Rmax
National standards stipulate that three indicators are commonly used to evaluate surface roughness (unit: μm): the average arithmetic deviation of the profile Ra, the average height of unevenness Rz and the maximum height Ry. Ra indicator is often used in actual production. The maximum micro height deviation Ry of the contour is usually expressed by the Rmax symbol in Japan and other countries, and the VDI index is commonly used in Europe and America. The following is the comparison table of VDI3400, Ra, Rmax.
VDI3400, Ra, Rmax comparison table
3. Factors forming surface roughness
Surface roughness is generally formed by the processing method used and other factors, such as the friction between the tool and the surface of the part during the processing, the plastic deformation of the surface layer metal when the chips are separated, and the high-frequency vibration in the process system, electrical processing Discharge pits and so on. Due to the difference in processing methods and workpiece materials, the depth, density, shape and texture of the traces left on the processed surface are different.
4. The main performance of the influence of surface roughness on parts
Affect wear resistance. The rougher the surface, the smaller the effective contact area between the mating surfaces, the greater the pressure, the greater the frictional resistance, and the faster the wear.
Affect the stability of coordination. For clearance fits, the rougher the surface, the easier it is to wear, which will gradually increase the clearance during work; for interference fits, the microscopic peaks are flattened during assembly, which reduces the actual effective interference and reduces The connection strength.
Affect fatigue strength. There are large wave troughs on the surface of rough parts. Like sharp notches and cracks, they are very sensitive to stress concentration, thereby affecting the fatigue strength of the parts.
Affect corrosion resistance. The surface of rough parts can easily cause corrosive gas or liquid to penetrate into the inner metal layer through the microscopic valleys on the surface, causing surface corrosion.
Affect sealing. Rough surfaces cannot be closely attached, and gas or liquid leaks through the gaps between the contact surfaces.
Affect contact stiffness. Contact stiffness is the ability of the joint surface of the part to resist contact deformation under the action of external force. The stiffness of the machine largely depends on the contact stiffness between the parts.
Affect 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 during precision measurement.
In addition, the surface roughness will have varying degrees of influence on the coating, thermal conductivity and contact resistance, reflectivity and radiation performance of the parts, the resistance of liquid and gas flow, and the flow of current on the conductor surface.
5. Evaluation basis for surface roughness
1. Sampling length
The sampling length L is the length of a reference line specified for evaluating the surface roughness. According to the actual surface formation and texture characteristics of the part, the length that can reflect the characteristics of the surface roughness should be selected, and the sampling length should be measured according to the general trend of the actual surface contour. The purpose of specifying and selecting the sampling length is to limit and reduce the influence of surface waviness and shape errors on the measurement results of surface roughness. Commonly used options for roughness meters are generally: 0.25mm, 0.8mm, 2.5mm
2. Evaluation length
The evaluation length is a length necessary to evaluate the contour, and it can include one or several sampling lengths. Because the surface roughness of each part of the part surface is not necessarily very uniform, a certain surface roughness characteristic cannot be reflected reasonably in a sampling length, so 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, when the evaluation length is 5L, 5X0.8=4mm
3. Baseline
The baseline is the contour centerline used to evaluate the surface roughness parameters. There are two types of reference lines: the minimum square of the contour: within the sampling length, the sum of the squares of the contour offset of each point on the contour line is the smallest, and it has a geometric contour shape. The arithmetic mean centerline of the contour: within the sampling length, the area of the upper and lower contours on the centerline is equal. In theory, the *small squares center line is an ideal baseline, but it is difficult to obtain in practical applications. Therefore, it is generally replaced by the arithmetic mean center line of the contour, and a straight line with an approximate position can be used for 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, and the measurement stroke is 5L+2L=7L. The measurement stroke is 7X0.8=5.6mm. Know this It is very important to calculate the distance moved on the workpiece. So as to determine the contact surface size of the smallest workpiece measured by the user.
6. Surface roughness evaluation parameters
1. Height characteristic parameters
Ra contour arithmetic mean deviation: the arithmetic mean of the good value of contour deviation within the sampling length (lr). In actual measurement, the more the number of measurement points, the more accurate Ra is.
Rz Maximum contour height: the distance between the top line of the contour and the bottom line of the valley.
In the common range of amplitude parameters, Ra is preferred. Before 2006, there was also an evaluation parameter in the national standard, which was “the ten-point height of micro-roughness” represented by Rz, and the maximum height of the contour was represented by Ry. After 2006, the national standard canceled the ten-point height of micro-roughness and adopted Rz represents the maximum height of the profile.
2. Spacing characteristic parameters
Rsm The average width of contour elements. Within the sampling length, the average value of the profile microscopic unevenness spacing. The microscopic unevenness distance refers to the length of the profile peak and the adjacent profile valley on the midline. In the case of the same Ra value, the Rsm value is not necessarily the same, so the reflected texture will also be different. Surfaces that value texture usually pay attention to the two indicators of Ra and Rsm.
The Rmr shape characteristic parameter is expressed by the contour support length ratio, which is the ratio of the contour support length to the sampling length. The contour support length is the sum of the length of each section of the cross section obtained when a straight line parallel to the center line and a distance c from the top of the contour line meets the contour within the sampling length.
7. Surface roughness measurement method
1. Comparative method
It is used for on-site measurement in the workshop, and is often used for the measurement of medium or rough surfaces. The method is to compare the measured surface with a roughness model marked with a certain value to determine the measured surface roughness value.
2. Stylus method
The surface roughness uses a diamond stylus with a tip curvature radius of about 2 microns to slide slowly along the measured surface. The up and down displacement of the diamond stylus is converted into an electrical signal by an electrical length sensor, which is indicated by the display instrument after amplification, filtering, and calculation The surface roughness value can also be used to record the profile curve of the measured section. Generally, the measuring tool that can only display the surface roughness value is called the surface roughness measuring instrument, and the surface roughness profiler that can record the surface profile curve at the same time. Both of these measuring tools have electronic calculation circuits or electronic computers, which can automatically calculate the arithmetic mean deviation Ra of the contour, the ten-point height of the microscopic unevenness Rz, the maximum height of the contour Ry and other various evaluation parameters, which have high measurement efficiency and are applicable To measure the surface roughness of Ra of 0.025～6.3 microns.
3. Light section method
The light band formed by the light passing through the slit is projected onto the surface to be measured, and the surface roughness is measured by the contour curve formed by the intersection of the light with the surface to be measured (Figure 3). After the light emitted by the light source passes through the condenser, the slit, and the 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 enlarged by the objective lens 2 and projected to Reticle. Use the micrometer eyepiece and the reading drum to read the h value first, and then calculate the H value. The surface roughness measurement tool using this method is called a light section microscope. It is suitable for measuring the surface roughness with RZ and Ry of 0.8-100 micrometers, and it needs to manually pick points, and the measurement efficiency is low.
4. Interference method
Use the principle of light wave interference (see flat crystal, laser length measurement technology) to display the shape error of the measured surface as interference fringe patterns, and use a microscope with high magnification (up to 500 times) to enlarge the microscopic parts of these interference fringes Perform measurement to get the surface roughness to be measured. The surface roughness measurement tool using this method is called an interference microscope. This method is suitable for measuring surface roughness with Rz and Ry of 0.025 to 0.8 microns.
8. Selection of surface roughness
The selection of surface roughness parameters should not only meet the functional requirements of the surface of the part, but also consider economic rationality. For specific selection, please refer to the existing drawings of similar parts and determine by analogy. On the premise of meeting the functional requirements of the parts, a larger surface roughness parameter value should be selected as much as possible to reduce the processing cost. Generally speaking, the working surface, mating surface, sealing surface, friction surface with high moving speed and high unit pressure, etc., have high requirements for the smoothness of the surface, and the parameter value should be smaller. For non-working surfaces, non-matching surfaces, and surfaces with low dimensional accuracy, the parameter value should be the relationship between the parameter Ra value and the processing method and its application examples, which can be used for reference when selecting.
