Press fit force is calculated by interference measurement
Publish: 2021-04-29 10:52:15
1. Press fit force involves many factors, the calculation is more complex
can refer to the standard: GB / T 5371-2004 limit and fit, calculation and selection of interference fit
if you can't find the email, I'll send you a , I have it here
can refer to the standard: GB / T 5371-2004 limit and fit, calculation and selection of interference fit
if you can't find the email, I'll send you a , I have it here
2. The copper sleeve with interference of 0.05 needs at least 10 tons of press to press the copper sleeve in. This kind of assembly method is not as good as the cold assembly method. If you put the Rongchang copper sleeve into the freezer and then put it in, it will be more difficult to damage the copper sleeve. The copper sleeve is still very round and increases the service life of the copper sleeve.
3. If you want to scare people away, you can pass one of their sizes when you are under the pressure of settlement ring the Chinese New Year
4. The interference you design is the function of transmitting torque. Prevent relative movement between bearing inner ring and shaft diameter!
5. I'm late ~
"master" hopes to add several conditions: the shape and size of the structure around the hole, the material and heat treatment status of the hole and shaft, and the lubrication conditions. In addition, "the aperture is 6.58mm, the interference is 10mm", is it too exaggerated? Please clarify.
"master" hopes to add several conditions: the shape and size of the structure around the hole, the material and heat treatment status of the hole and shaft, and the lubrication conditions. In addition, "the aperture is 6.58mm, the interference is 10mm", is it too exaggerated? Please clarify.
6. I'm late ~
"master" hopes to add several conditions: the structural shape and size around the hole, the material and heat treatment status of the hole and shaft, and the lubrication conditions. In addition, "the aperture is 6.58mm, and the interference is 10mm", is that too exaggerated? Please clarify
"master" hopes to add several conditions: the structural shape and size around the hole, the material and heat treatment status of the hole and shaft, and the lubrication conditions. In addition, "the aperture is 6.58mm, and the interference is 10mm", is that too exaggerated? Please clarify
7. The relationship between the tolerance zones of the combined holes and shafts with the same basic dimensions. Determine the tightness of the combination. The algebraic difference obtained by subtracting the size of the matching shaft from the size of the hole is called clearance when it is positive, interference when it is negative, and sometimes interference is called negative clearance. According to the relationship of tolerance zone between hole and shaft, that is, the characteristics of clearance, interference and its variation, fit can be divided into three situations: ① clearance fit. The tolerance zone of the hole is above the tolerance zone of the shaft and has a fit with clearance (including minimum clearance equal to zero). The function of clearance is to store lubricating oil and compensate various errors. The size of clearance affects the relative motion of hole and shaft. Clearance fit is mainly used for the movable connection between holes and shafts, such as the connection between sliding bearing and shaft. ② Interference fit. The tolerance zone of the hole is under the tolerance zone of the shaft and has the fit of interference (including the minimum interference equal to zero). In interference fit, because the size of the shaft is larger than the size of the hole, it needs to be assembled by means of pressure or thermal expansion and cold contraction. Interference fit is mainly used for the tight connection between the hole shaft which does not allow relative movement, such as the connection between the ring gear of large gear and the hub. ③ Transition coordination. The tolerance zones of the hole and shaft overlap each other, which may have clearance or interference fit (the clearance and interference are generally small). Transition fit is mainly used for positioning connection which requires better alignment and coaxiality between hole shafts and is easy to disassemble and assemble, such as the connection between inner diameter of rolling bearing and shaft
the inner diameter and outer diameter radial displacement of high-speed motorized spindle bearing inner ring width and wall thickness are far less than its diameter, so it can be simplified as a thin-walled ring and solved according to the plane stress problem [6-7]; The hollow spindle can be simplified as a thick wall cylinder and solved according to the plane strain problem [5]. The radial centrifugal displacement of high-speed rotating rotor is caused by inertial force, and its equilibrium differential equation in polar coordinates is [8]: D σ rdr+ σ r- σθ r+ ρω Where 2R = 0 (1) σ r, σθ It represents radial and circumferential normal stress respectively ρ Rotor material density ω The physical equation under the plane stress of rotational angular velocity is as follows: σ r=E1- μ 2(dr+ μ ur)(2) σθ= E1- μ 2(ur+ μ DR) (3) the physical equation under plane strain is as follows: σ r=E(1- μ)( 1+ μ)( 1-2 μ)( dr+ μ 1- μ ur)(4) σθ= E(1- μ)( 1+ μ)( 1-2 μ)( ur+ μ 1- μ DR) (5) where u, radial displacement e, μ It represents the elastic molus of rotor material and Poisson's ratio 1.1 respectively. The radial displacement of bearing inner diameter is obtained by substituting formula (2) and (3) into formula (1), and the formula is: r2d2udr2 + rdr-u = - 1- μ 2E ρω The solution of 2r3 (6) is: u = C1r + c2r-1- μ 28E ρω 2r3 (7) as shown in Fig. 1, for the bearing inner ring rotating at high speed, assume the stress analysis of bearing inner ring in Fig. 1 and the stress analysis of main shaft in Fig. 2, the groove and inner and outer diameter surface are not stressed, and the inner diameter surface is installed on the main shaft with interference, bearing uniform pressure P. The nominal inner diameter is D, and the inner groove dimension Di is used to approximate the outer diameter of the ring in the model, the elastic molus EB and Poisson's ratio of the material μ b. Density ρ b. The angular velocity of rotation is ω By boundary conditions σ r|r=di2=0, σ When R | r = D2 = - P, C1 and C2 can be obtained and substituted into formula (7), when r = D2, the radial displacement of inner ring inner diameter can be obtained as: UB (r = D2) = (1)- μ b)d3+(1+ μ b)dd2i2Eb(d2i-d2)p+( μ b+3)dd2i+(1- μ b)d332Eb ρ b ω 2 (8) 1.2 by substituting formula (4) and (5) into formula (1), it is obtained that r2d2udr2 + rdr-u = - (1)+ μ)( 1-2 μ) E(1- μ)ρω The solution of 2r3 (9) is: u = C1r + C2R - (1)+ μ)( 1-2 μ) 8E(1- μ)ρω 2r3 (10) as shown in Figure 2, the outer diameter of the hollow spindle is subject to the matching pressure P, the inner surface is free, the nominal sizes of the outer diameter and the inner hole are D and DS respectively, the material elastic molus es and Poisson's ratio μ s. Density ρ s. The angular velocity of rotation is ω By boundary conditions σ r|r=d2=-p, σ When R | r = DS2 = 0, C1 and C2 can be obtained and substituted into formula (10). When r = D2, the radial displacement of the outer diameter of the spindle can be obtained as: US (r = D2) = (1)+ μ s)d[d2s+(1-2 μ s)d2]2Es(d2s-d2)p+(1+ μ s)d[(3-2 μ s)d2s+(1-2 μ s)d2]32Es・ ρ s ω 2 (11) 2 the amount of interference required for the fit of high-speed motorized spindle bearing and spindle 2.1 the amount of interference required when considering centrifugal force. The fit of bearing inner ring and spindle is shown in Fig. 3. When the bearing inner ring and spindle in Fig. 3 rotate at high speed, on the one hand, e to the effect of centrifugal force, the inner hole of bearing inner ring will expand and the outer diameter of spindle will expand, resulting in the change of interference; On the other hand, the inner diameter of the bearing inner ring increases e to the action of the matching pressure P, while the outer diameter of the spindle decreases. At this time, the amount of interference required for the inner ring of the bearing to fit with the spindle can be calculated as follows: I '= 2 [UB (r = D2) - US (r = D2)] = [(1)- μ b)d3+(1+ μ b)dd2iEb(d2i-d2)-(1+ μ s)dd2s+(1+ μ s)(1-2 μ s)d3Es(d2s-d2)]p+[( μ b+3)dd2i+(1- μ b)d316Eb ρ b-(1+ μ s)(3-2 μ s)dd2s+(1+ μ s)(1-2 μ s)d316Es ρ s] ω 2 = is + IL (12), where the former term is the static interference, which is proportional to the pressure between the mating surfaces, and the minimum pressure required between the mating surfaces is proportional to the maximum torque transmitted by the motorized spindle [9]; The latter term IL in equation (12) is the interference required e to the centrifugal force acting on the inner ring and the spindle, which is proportional to the square of the spindle speed. 2.2 influence of temperature change on interference value when the motorized spindle rotates at high speed, the motor loss and bearing friction heat increase the temperature of the spindle and bearing, so the bearing inner ring and spindle will have radial thermal expansion. Due to the different temperatures of the spindle and bearing, the linear expansion coefficient of materials may also be different, which will change the interference value. If the temperature distribution between the spindle and the inner ring is uniform, the inner diameter of the bearing inner ring will increase in the inner ring temperature Δ The results show that the radial thermal displacement UBT and the outer diameter of the spindle under the action of TB increase with the temperature rise of the spindle Δ The radial thermal displacement ust under the action of TS can be calculated by formula (13) and (14) respectively [10]: UBT= α b Δ Tbd(13)usT= α s Δ Ts(1+ μ s) Where d (14) α b, α s. Therefore, the change value of the interference between the spindle and the bearing inner ring caused by the temperature rise is: it = 2 (UBT UST) = 2[ α b Δ Tb- α s Δ Ts(1+ μ s) [D (15) 2.3 the total interference I is mainly composed of static interference, centrifugal interference and temperature rise interference, and is also affected by radial load, surface roughness and other factors. In this paper, only the first three parts are discussed, then: I = is + IL + it (16) 3 calculation example, taking the motorized spindle developed by the national high efficiency grinding engineering center as an example, the bearing and its matching spindle parameters are d = 65mm, di = 7115mm, DS = 35mm; The bearing is preloaded under constant pressure, with preload of 300N, oil air lubrication, and working temperature of 25 ℃. The elastic molus, Poisson's ratio, density and coefficient of linear expansion of steel are E1 = 2106 × 1011Pa, μ 1=013, ρ 1=718 × 103kg/m3, α 1=1215 × 10-61/℃; The elastic molus, Poisson's ratio, density and coefficient of linear expansion of Si3N4 ceramics are E2 = 312 × 1011Pa, μ 2=0126, ρ 2=312 × 103kg/m3, α 2=312 × 10-61/℃ Taking the bearing, the spindle and the bearing seat as a system, the temperature of the steel spindle and the matched steel spindle when the inner ring of the bearing is made of steel or ceramic is calculated by using the node network method [11], as shown in Fig. 4 and Fig. 5. Fig. 4 the influence of rotational speed on the temperature of steel inner ring and spindle Fig. 5 the influence of rotational speed on the temperature of ceramic inner ring and spindle the centrifugal interference IL and temperature rise interference it required for the matching of steel and ceramic bearing inner ring with steel spindle are calculated by equation (12) and equation (15), respectively, as shown in Fig. 6 and Fig. 7. At the same time, considering the centrifugal force and temperature rise, the required amount of interference is shown in Figure 8. Fig. 6 the effect of rotational speed on the required centrifugal interference;
the inner diameter and outer diameter radial displacement of high-speed motorized spindle bearing inner ring width and wall thickness are far less than its diameter, so it can be simplified as a thin-walled ring and solved according to the plane stress problem [6-7]; The hollow spindle can be simplified as a thick wall cylinder and solved according to the plane strain problem [5]. The radial centrifugal displacement of high-speed rotating rotor is caused by inertial force, and its equilibrium differential equation in polar coordinates is [8]: D σ rdr+ σ r- σθ r+ ρω Where 2R = 0 (1) σ r, σθ It represents radial and circumferential normal stress respectively ρ Rotor material density ω The physical equation under the plane stress of rotational angular velocity is as follows: σ r=E1- μ 2(dr+ μ ur)(2) σθ= E1- μ 2(ur+ μ DR) (3) the physical equation under plane strain is as follows: σ r=E(1- μ)( 1+ μ)( 1-2 μ)( dr+ μ 1- μ ur)(4) σθ= E(1- μ)( 1+ μ)( 1-2 μ)( ur+ μ 1- μ DR) (5) where u, radial displacement e, μ It represents the elastic molus of rotor material and Poisson's ratio 1.1 respectively. The radial displacement of bearing inner diameter is obtained by substituting formula (2) and (3) into formula (1), and the formula is: r2d2udr2 + rdr-u = - 1- μ 2E ρω The solution of 2r3 (6) is: u = C1r + c2r-1- μ 28E ρω 2r3 (7) as shown in Fig. 1, for the bearing inner ring rotating at high speed, assume the stress analysis of bearing inner ring in Fig. 1 and the stress analysis of main shaft in Fig. 2, the groove and inner and outer diameter surface are not stressed, and the inner diameter surface is installed on the main shaft with interference, bearing uniform pressure P. The nominal inner diameter is D, and the inner groove dimension Di is used to approximate the outer diameter of the ring in the model, the elastic molus EB and Poisson's ratio of the material μ b. Density ρ b. The angular velocity of rotation is ω By boundary conditions σ r|r=di2=0, σ When R | r = D2 = - P, C1 and C2 can be obtained and substituted into formula (7), when r = D2, the radial displacement of inner ring inner diameter can be obtained as: UB (r = D2) = (1)- μ b)d3+(1+ μ b)dd2i2Eb(d2i-d2)p+( μ b+3)dd2i+(1- μ b)d332Eb ρ b ω 2 (8) 1.2 by substituting formula (4) and (5) into formula (1), it is obtained that r2d2udr2 + rdr-u = - (1)+ μ)( 1-2 μ) E(1- μ)ρω The solution of 2r3 (9) is: u = C1r + C2R - (1)+ μ)( 1-2 μ) 8E(1- μ)ρω 2r3 (10) as shown in Figure 2, the outer diameter of the hollow spindle is subject to the matching pressure P, the inner surface is free, the nominal sizes of the outer diameter and the inner hole are D and DS respectively, the material elastic molus es and Poisson's ratio μ s. Density ρ s. The angular velocity of rotation is ω By boundary conditions σ r|r=d2=-p, σ When R | r = DS2 = 0, C1 and C2 can be obtained and substituted into formula (10). When r = D2, the radial displacement of the outer diameter of the spindle can be obtained as: US (r = D2) = (1)+ μ s)d[d2s+(1-2 μ s)d2]2Es(d2s-d2)p+(1+ μ s)d[(3-2 μ s)d2s+(1-2 μ s)d2]32Es・ ρ s ω 2 (11) 2 the amount of interference required for the fit of high-speed motorized spindle bearing and spindle 2.1 the amount of interference required when considering centrifugal force. The fit of bearing inner ring and spindle is shown in Fig. 3. When the bearing inner ring and spindle in Fig. 3 rotate at high speed, on the one hand, e to the effect of centrifugal force, the inner hole of bearing inner ring will expand and the outer diameter of spindle will expand, resulting in the change of interference; On the other hand, the inner diameter of the bearing inner ring increases e to the action of the matching pressure P, while the outer diameter of the spindle decreases. At this time, the amount of interference required for the inner ring of the bearing to fit with the spindle can be calculated as follows: I '= 2 [UB (r = D2) - US (r = D2)] = [(1)- μ b)d3+(1+ μ b)dd2iEb(d2i-d2)-(1+ μ s)dd2s+(1+ μ s)(1-2 μ s)d3Es(d2s-d2)]p+[( μ b+3)dd2i+(1- μ b)d316Eb ρ b-(1+ μ s)(3-2 μ s)dd2s+(1+ μ s)(1-2 μ s)d316Es ρ s] ω 2 = is + IL (12), where the former term is the static interference, which is proportional to the pressure between the mating surfaces, and the minimum pressure required between the mating surfaces is proportional to the maximum torque transmitted by the motorized spindle [9]; The latter term IL in equation (12) is the interference required e to the centrifugal force acting on the inner ring and the spindle, which is proportional to the square of the spindle speed. 2.2 influence of temperature change on interference value when the motorized spindle rotates at high speed, the motor loss and bearing friction heat increase the temperature of the spindle and bearing, so the bearing inner ring and spindle will have radial thermal expansion. Due to the different temperatures of the spindle and bearing, the linear expansion coefficient of materials may also be different, which will change the interference value. If the temperature distribution between the spindle and the inner ring is uniform, the inner diameter of the bearing inner ring will increase in the inner ring temperature Δ The results show that the radial thermal displacement UBT and the outer diameter of the spindle under the action of TB increase with the temperature rise of the spindle Δ The radial thermal displacement ust under the action of TS can be calculated by formula (13) and (14) respectively [10]: UBT= α b Δ Tbd(13)usT= α s Δ Ts(1+ μ s) Where d (14) α b, α s. Therefore, the change value of the interference between the spindle and the bearing inner ring caused by the temperature rise is: it = 2 (UBT UST) = 2[ α b Δ Tb- α s Δ Ts(1+ μ s) [D (15) 2.3 the total interference I is mainly composed of static interference, centrifugal interference and temperature rise interference, and is also affected by radial load, surface roughness and other factors. In this paper, only the first three parts are discussed, then: I = is + IL + it (16) 3 calculation example, taking the motorized spindle developed by the national high efficiency grinding engineering center as an example, the bearing and its matching spindle parameters are d = 65mm, di = 7115mm, DS = 35mm; The bearing is preloaded under constant pressure, with preload of 300N, oil air lubrication, and working temperature of 25 ℃. The elastic molus, Poisson's ratio, density and coefficient of linear expansion of steel are E1 = 2106 × 1011Pa, μ 1=013, ρ 1=718 × 103kg/m3, α 1=1215 × 10-61/℃; The elastic molus, Poisson's ratio, density and coefficient of linear expansion of Si3N4 ceramics are E2 = 312 × 1011Pa, μ 2=0126, ρ 2=312 × 103kg/m3, α 2=312 × 10-61/℃ Taking the bearing, the spindle and the bearing seat as a system, the temperature of the steel spindle and the matched steel spindle when the inner ring of the bearing is made of steel or ceramic is calculated by using the node network method [11], as shown in Fig. 4 and Fig. 5. Fig. 4 the influence of rotational speed on the temperature of steel inner ring and spindle Fig. 5 the influence of rotational speed on the temperature of ceramic inner ring and spindle the centrifugal interference IL and temperature rise interference it required for the matching of steel and ceramic bearing inner ring with steel spindle are calculated by equation (12) and equation (15), respectively, as shown in Fig. 6 and Fig. 7. At the same time, considering the centrifugal force and temperature rise, the required amount of interference is shown in Figure 8. Fig. 6 the effect of rotational speed on the required centrifugal interference;
8.
Interference refers to the relationship between the combined hole and shaft tolerance zone with the same basic size. Determine the tightness of the combination. The algebraic difference obtained by subtracting the size of matching shaft from the size of hole is called clearance when it is positive, interference when it is negative, and sometimes interference is called negative clearance
fit can be divided into three cases:
① clearance fit. The tolerance zone of the hole is above the tolerance zone of the shaft and has a fit with clearance (including minimum clearance equal to zero). The function of clearance is to store lubricating oil and compensate various errors. The size of clearance affects the relative motion of hole and shaft. Clearance fit is mainly used for the movable connection between holes and shafts, such as the connection between sliding bearing and shaft
(2) interference fit. The tolerance zone of the hole is under the tolerance zone of the shaft and has the fit of interference (including the minimum interference equal to zero). In interference fit, because the size of the shaft is larger than the size of the hole, it needs to be assembled by means of pressure or thermal expansion and cold contraction. Interference fit is mainly used for the tight connection between the hole shaft which does not allow relative movement, such as the connection between the ring gear of large gear and the hub (3) transitional coordination. The tolerance zones of the hole and shaft overlap each other, which may have clearance or interference fit (the clearance and interference are generally small). Transition fit is mainly used for positioning connection which requires better alignment and coaxiality between hole shafts and is easy to disassemble and assemble, such as the connection between inner diameter of rolling bearing and shaft< br />Hot content