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Concise analysis and calculation of the manufacturing size of the repair ring

Abstract: This paper comprehensively analyzes three kinds of situations that affect the change of the closed ring when the repair ring is repaired, and deduces the concise calculation formula of the manufacturing size of the repair ring in various cases, so that the calculation of the repair method is more perfect, more economical, and simpler

key words: repair ring; Repair method; Assemble dimension chain; The calculation of assembly dimension chain is often encountered in the process of mechanical design and assembly of closed ring. When the repair method is adopted, the constituent rings in the dimension chain are manufactured according to economic accuracy. During assembly, a predetermined ring (repair ring) is supplemented according to the actual situation to meet the requirements of assembly accuracy. Therefore, the manufacturing size of the repair ring must be correctly calculated before assembly - not only to make the repair work possible (that is, to ensure sufficient repair quantity), but also to minimize the repair workload (that is, the most economical)

1 analysis of the impact on the size of the closed ring when the repair ring (or repair surface) is repaired

1.1 the repair ring (surface) is repaired to make the size of the closed ring smaller

in the assembly relationship shown in Figure 1 (a), if the base plate A2 is selected as the repair ring, A2 will be reduced regardless of the upper and lower parts of A2, so as to make the closed ring A0 smaller (A2 is an increase ring); In the assembly relationship shown in Figure 1 (c), if the pressing plate A3 is selected as the repair ring and the M surface of A3 is designated as the repair surface, the M surface is repaired and A3 is reduced, so that the closed ring A0 becomes smaller (A3 is an increased ring)

figure 1

1.2 the repair ring (surface) is repaired to increase the size of the closed ring

in the assembly relationship shown in Figure 1 (b), if axis A2 is a repair ring, A2's own size is reduced when it is repaired, because A2 is a reduced ring, so the closed ring A0 becomes larger; As shown in Figure 1 (c), if the N surface of A3 is designated as the repair surface, the N surface is repaired to make the size of A3 larger, so as to make the closing ring A0 larger

1.3 different surfaces of the repair ring are repaired to make the closed ring smaller and larger

as shown in Figure 1 (c), A3 is the repair ring. If both M and n sides of A3 can be used as the repair ring, A0 will be smaller when repairing m surface and larger when repairing n surface

2 analysis and calculation of manufacturing dimensions of repair rings

when the repair method is adopted, the tolerance of each component ring has been enlarged to the extent of economic feasibility, that is, it is manufactured according to economic machining accuracy. In this way, the tolerance t0 of the actual closed ring A0 formed after direct assembly is bound to be greater than the tolerance t '0 of a' 0 required by the assembly accuracy. For out of tolerance assembly, it should be able to return to the specified range by repairing the ring chimney dust emission concentration display value of 8mg/nm3~10mg/nm3. Therefore, the manufacturing size of the repair ring before repair must ensure the possibility of repair after direct assembly, that is, there is enough repair quantity, and no scrap that cannot be repaired is allowed

2.1 analysis and calculation of the closed ring when the repair ring (surface) is repaired

as the closed ring (surface) is repaired, the closed ring becomes smaller and smaller as it is repaired, the limit size of the repair ring must not be underestimated. The viability certificate of Chinese private enterprises must not be underestimated. The minimum limit of the actual closed ring is not less than the minimum limit required for assembly, that is,

a0min ≥ a ′ 0min (1)

a0 and a ′ 0 should be shown in Figure 2 (a), Ensure that any assembly result can meet A0 ≥ a ′ 0min. For the assembly of A0 ≥ a ′ 0max, the repair ring can be repaired to reduce A0 to a ′ 0max and become qualified. As shown in Figure 2 (b), it is not allowed that A0 ＜ a ′ 0min assembly may occur and waste products may be generated

Figure 2 the relationship between A0 and a '0 when the repair ring (surface) is sealed and the closed loop becomes smaller.

according to the principle of ensuring that the repair amount is sufficient and minimum, there should be

a0min = a' 0min+zmin (2)

where: Zmin represents the minimum repair amount that must be carried out when there are special requirements for assembly, and zmin=0 can be taken when there are no requirements

from the basic formula of the size chain extreme value algorithm

into equation (2), there is

in which: AP is an increasing ring; AQ is minus ring; M is the number of rings increased; N is the total number of rings including closed rings. In formula (3), except that the repair ring is unknown, the rest are known or determined, so a limit size of the repair ring can be directly calculated. If the repair ring AK is an increasing ring, it can be separated from the increasing ring group to obtain

if the repair ring is a decreasing ring, it can be separated from the decreasing ring group to obtain

the tolerance of the repair ring has been determined according to the economic accuracy, so it is not difficult to calculate another limit dimension

the maximum repair amount Zmax can be calculated from Figure 2 (a):

2.2 analysis and calculation when the repair ring (surface) is repaired to make the closed ring larger

because the repair ring (surface) is repaired, the closed ring becomes larger and larger, so it must be ensured that the maximum limit of the actual closed ring is not greater than the maximum limit required for assembly, that is,

a0max ≤ a ′ 0max (5)

a0 and a ′ 0 should have the position relationship as shown in Figure 3 (a). As shown in Figure 3 (b), it is not allowed to produce scrap that cannot be repaired

Figure 3 the relationship between A0 and a '0 when the repair ring (surface) is sealed and the closed loop becomes larger

according to the principle of ensuring that the repair amount is sufficient and minimum, there should be

a0max=a' 0max Zmin (6)

that is,

the maximum limit size (if the ring is increased) or the minimum limit size (if the ring is decreased) of the repair ring can be obtained directly from formula (7). Another limit dimension of the repair ring can be obtained from its tolerance

the maximum repair amount Zmax can be calculated from Figure 3 (a):

2.3 analysis and calculation when different surfaces of the repair ring are repaired to make the closed ring small and large

at this time, if the two surface areas of the repair ring differ greatly or the difficulty of repair differs greatly, the side with smaller area and easy repair should be designated as the repair surface, and then the influence on the closed ring should be judged according to the single repair surface, and then calculated with the corresponding formula

if both surfaces of the repair ring are easy to repair and the repair workload is equal, both surfaces should be selected as the repair surface at the same time. As shown in Figure 1 (c), select the M and n sides of A3 at the same time as the repair surface. When A0> a ′ 0max after direct assembly, trim m surface to reduce A0 until it is qualified; When A0 ＜ a ′ 0min, repair n surface to make A0 increase to qualified. Therefore, no matter what, there is no waste product that cannot be repaired, but to meet the condition of minimum repair workload, it should be made that

a0m=a ′ 0m (9)

and

therefore,

the average size AKM of the repair ring can be directly calculated from formula (10), so ak=akm ± tk/2

the maximum repair amount Zmax can be obtained from figure 4:

compared with formula (4) or (8) when one side is repaired, the maximum repair amount at this time is reduced by half

the above calculation can also be directly carried out with deviation. Just use the maximum limit dimension Amax, the minimum limit dimension Amin and the average dimension am in each formula with the corresponding upper deviation es, lower deviation EI and average deviation respectively Δ Replace it. When calculating with deviation, the basic dimension of the repair ring should be calculated from the following formula:

Figure 4 the relationship between A0 and a '0 when the two sides of the repair ring are sealed and the closed loop is variable

3 the steps and application examples of solving the dimension chain by the repair method

taking Figure 1 (c) as an example, it is required to ensure that the gap between the pressure plate and the guide rail after assembly a0=0.02 ~ 0.06mm. A1=30mm, a2=20mm, a3=10mm are known. The repair method is adopted for assembly, and the minimum repair amount is taken as zero. Try to determine the manufacturing size and limit deviation of each ring, and calculate the maximum repair quantity

solution:

a. establish the assembly dimension chain

as shown in Figure 5, according to the meaning of the topic, A1, A2 and A3 are the constituent rings of the assembly dimension chain, and A0 is the closed ring. The closing ring meeting the assembly requirements shall be a ′ 0=0.02 ~ 0.06mm

Figure 5 assembly dimension chain

b. determine the repair ring and repair surface

the repair ring and repair surface should meet the following conditions: ① the shape of the part is relatively simple, easy to assemble and disassemble, easy to repair, and the repair area is small; ② It should not be a common ring of multiple dimension chains. A3 should be selected as the repair ring. Both sides m and N of A3 should be repaired, so both sides are determined to be repaired

c. determine the manufacturing tolerance of each ring

according to the economic machining accuracy, it is determined as follows: t1=0 Don't worry. 1mm, t2=0.2mm, t3=0.1mm. So

d. determine the limit deviation of the manufacturing dimension of each ring (except for the repair surface)

according to the "in body principle", it is determined as follows: a1= 1mm，A2=20+0.20mm。

e. calculate the manufacturing size and limit deviation of the repair ring

since m and N surfaces are both repair surfaces, and as mentioned above, A0 decreases when repairing m surface and increases when repairing n surface, so it belongs to the third case, so it should be Δ 0= Δ′ 0, i.e.

Δ 0= Δ 2+ Δ 3- Δ 1= Δ′ 0 (13)

where: Δ′ 0=(ES′0+EI′0)/2=0.04(mm)， Δ 1=(ES1+EI1)/2=-0.05(mm)， Δ 2= (es2+ei2)/2=0.1 (mm), substitute into equation (13) to get

Δ 3=-0.11 (mm)

so Es3= Δ 3+T3/2=-0.11+0.1/2=-0.06(mm)

EI3= Δ 3-T3/2=-0.. 1/2=-0.16 (mm)

and a0=a2+a3-a1=0

so a3=0+a1-a2===10 (mm)

that is,

a3= 16mm

f. calculate the maximum repair amount

zmax= (t0-t '0)/2= (0..04)/2=0.18 (mm)

in this case, if the m-surface is modified only, it should be analyzed and calculated according to the first case, and a3=10+0.12+0.02mm can be obtained; If n-PLANE is modified only, analyze and calculate according to the second case, and a3= 34mm。 In both cases, zmax=t0-t ′ 0=0.36 (mm)

4 conclusion

a. the calculation, analysis and formula of the manufacturing size of the repair ring introduced in this paper are concise and very characteristic. No matter whether the repair ring is an increasing ring or a decreasing ring, and whether the minimum repair amount is zero or not, it only needs to determine the influence of the repair surface on the change of the closed ring when it is repaired, and accurately use the corresponding formula, you can directly calculate the limit size or limit deviation of the repair ring. The calculation is simple and not easy to make mistakes

b. it is very important for the repair method to reasonably select the repair ring and specify the repair surface when necessary. Especially when the two sides of the repair ring are repaired and have different effects on the closed ring, it should be treated with caution to make the repair work the most economical

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