Calculation formula of additional axial force of bearing
Publish: 2021-05-13 12:12:29
1. If the shaft is placed horizontally and the disc has no other connectors, the static radial load is: the gravity (about: mass x9.8) n on the disc. The static and dynamic radial loads are related to the contact angle between the roller and raceway.
2. 5 Calculation of radial load ft and axial load FA of angular contact ball bearing and tapered roller bearing
when the equivalent dynamic load P of each bearing is calculated according to equation (13-8a), the radial load f is the radial load generated on each bearing by the radial force F acting on the shaft from the outside; However, the axial load F. is not completely generated by the external axial force F, but should be obtained according to the balance condition between the axial load on the whole shaft (including the derived axial force F e to the radial load f). Let's analyze this problem
according to the radial balance condition of the force, it is easy to calculate the radial load f.. FA on the two bearings from the radial force F acting on the shaft from the outside. When the magnitude and position of F are determined, the radial load f.. F. That's for sure. By F., F. Derived axial forces F, F. The size of can be calculated according to the formula in table 13-7. The calculated value of F, is equivalent to the normal installation condition, that is, it is approximately equivalent to that all the rolling elements of the lower half circle are loaded (the actual working condition of the bearing is not allowed to be less than this
2. The other end is marked as bearing 1. Take the shaft and its matching bearing inner ring as the separating body, if the axial balance is achieved, it should meet the requirements of
F. + FA = FA
If FA and F are obtained according to the formula in table 13-7. When the above relation is not satisfied, the following two situations will appear:
when f u+ F& gt; F The shaft has a tendency to move to the left, which is equivalent to that bearing 1 is "pressed" and bearing 2 is "relaxed". But in fact, the shaft must be in a balanced position (that is, the bearing seat must exert an additional axial force through the bearing elements to prevent the shaft from moving), so the total axial force F on the "pressed" bearing 1. Must be with F. + F. Phase equilibrium, i.e.
F = F. + F.
when the equivalent dynamic load P of each bearing is calculated according to equation (13-8a), the radial load f is the radial load generated on each bearing by the radial force F acting on the shaft from the outside; However, the axial load F. is not completely generated by the external axial force F, but should be obtained according to the balance condition between the axial load on the whole shaft (including the derived axial force F e to the radial load f). Let's analyze this problem
according to the radial balance condition of the force, it is easy to calculate the radial load f.. FA on the two bearings from the radial force F acting on the shaft from the outside. When the magnitude and position of F are determined, the radial load f.. F. That's for sure. By F., F. Derived axial forces F, F. The size of can be calculated according to the formula in table 13-7. The calculated value of F, is equivalent to the normal installation condition, that is, it is approximately equivalent to that all the rolling elements of the lower half circle are loaded (the actual working condition of the bearing is not allowed to be less than this
2. The other end is marked as bearing 1. Take the shaft and its matching bearing inner ring as the separating body, if the axial balance is achieved, it should meet the requirements of
F. + FA = FA
If FA and F are obtained according to the formula in table 13-7. When the above relation is not satisfied, the following two situations will appear:
when f u+ F& gt; F The shaft has a tendency to move to the left, which is equivalent to that bearing 1 is "pressed" and bearing 2 is "relaxed". But in fact, the shaft must be in a balanced position (that is, the bearing seat must exert an additional axial force through the bearing elements to prevent the shaft from moving), so the total axial force F on the "pressed" bearing 1. Must be with F. + F. Phase equilibrium, i.e.
F = F. + F.
3. If only the axial force inside the bearing is considered, there are: FA1 & gt; Fa2
please accept, thank you!
please accept, thank you!
4. The simple algorithm is resultant force, and the vector algorithm can be used for precise points
5. 1 Check calculation of fatigue life of imported rolling bearing I. Basic rated life and basic rated dynamic load
for a single rolling bearing, the so-called NSK bearing life refers to the number of revolutions that one ring can run relative to another ring before fatigue pitting of one ring or rolling element material for the first time
since the fatigue life of rolling bearings is quite discrete under the same working conditions for the same batch of bearings (identical structure, size, material, heat treatment and processing, etc.), the basic rated life can only be used as the standard for selecting bearings
Basic rated life: refers to the total number of revolutions (in revolutions) of a batch of NTN bearings that can operate under the same conditions, of which 90% can operate before fatigue pitting occurs, or the total working hours at a certain speed
Basic rated dynamic load C: the load value that the bearing can bear when the basic rated life of the bearing is 60 rpm. The basic rated dynamic load, for radial fag bearing, refers to the pure radial load, which is also called the radial basic rated dynamic load, expressed in; For the thrust bearing, it refers to the pure axial load, which is also called the axial basic rated dynamic load, expressed in; Diagonal contact ball bearing or tapered roller bearing refers to the radial component of the load which only proces pure radial displacement between the rings
different types of bearings have different basic dynamic load ratings, which represent the bearing capacity of different types of bearings. 2、 Figure 9-7 load life curve of Nachi bearing figure 9-7 is the load life curve of bearing, which shows the relationship between load P and basic rated life. The curve is expressed as:
(rotation) (9-1)
where p is the equivalent dynamic load (n)< br /> ε Is the life index for ball bearings ε ＝ 3 For roller bearings ε ＝ 10/3 In actual calculation, the commonly used hours to represent the bearing life are:
(H) (9-2)
where n is the rotational speed of INA Bearing (R / min)
the change of temperature usually has an impact on the material of bearing elements, the hardness of bearing will be reced, and the bearing capacity will be reced. Therefore, it is necessary to introce the temperature coefficient ft (see table 9-5) to modify the life calculation formula:
(rotation) (9-3)
(H) (9-4) table 9-5 temperature coefficient ft bearing working temperature (℃) ≤ 120 125 150 175 200 225 250 300 350
temperature coefficient ft 1.00 0.95 0.90 0.85 0.80 0.75 0.70 0.60.5 the constraint condition for fatigue life check calculation is
'
where: 39; The predicted life of Koyo bearing is listed in table 9-6 for reference
if the equivalent dynamic load P and speed n are known, the expected calculated life is 39; If it has also been selected, the basic dynamic load rating of the bearing can be calculated from formula (9-5) (?) 39; Value, so that the; Value: select the type of bearing required:
(9-5) Timken bearing expected calculated life recommended in table 9-6 machine type expected calculated life (H)
infrequently used instruments or equipment, such as gate opening and closing device, 300-3000
short-term or intermittent use of machinery, interruption of use will not cause serious consequences, such as manual machinery, 3000-8000
intermittent use of machinery, The consequences of interruption are serious, such as engine aided design, automatic transmission device of flow line, long-distance landing machine, workshop crane, rarely used machine tools and so on, which are 8000-12000
working 8 hours a day (the utilization rate is high), such as general gear drive, some fixed motors and so on, which are 12000-20000
working 8 hours a day (the utilization rate is not high), Such as metal cutting machine tools, continuous use cranes, wood processing machinery, printing machinery and other 20000-30000
24-hour continuous working machinery, such as mine lifts, textile machinery, pumps, motors and other 40000-60000
24-hour continuous working machinery, the consequences of interruption are serious. Such as fiber proction or papermaking equipment, power station main motor, mine water pump, ship propeller shaft, etc.
III. equivalent dynamic load of rolling bearing
Basic rated dynamic load of rolling IKO bearing for radial bearing, it refers to the radial load when the inner ring rotates and the outer ring is stationary, and for radial thrust bearing, it is the radial component of the load that makes the half ring of raceway loaded. For thrust bearings, the basic dynamic load rating is the central axial load. Therefore, the actual working load must be converted into equivalent dynamic load which is the same as the basic rated dynamic load condition before calculation. The equivalent dynamic load after conversion is an imaginary load, which is expressed by symbol. The bearing life under the action of equivalent dynamic load is equal to that under the action of actual load. Under the action of constant radial and axial loads, the calculation formula of equivalent dynamic load is:
(9-6a)
where: is the radial load (n) of the bearing, that is, the radial component of the actual load of the bearing
is the axial load (n) of the bearing, which is the axial component of the actual load of the bearing
is the radial load coefficient, which is the correction coefficient for converting the actual radial load into equivalent dynamic load, as shown in table 9-7
is the axial load factor, which is the correction factor for converting the actual axial load into equivalent dynamic load, as shown in table 9-7
for the radial cylindrical roller bearing, needle roller bearing and spiral roller bearing which can only bear the pure radial load:
= (9-6b)
for the thrust bearing which can only bear the pure axial load:
= (9-6c)
according to the actual working condition of the bearing, the load factor (table 9-8) should be introced to modify it, The modified equivalent dynamic load should be calculated according to the following formula:
= (+) (9-7a)
= (9-7b)
= (9-7c) table 9-8 load coefficient F P load property F P example
no impact or slight impact 1.0 ~ 1.2 motor, steam turbine, fan, water pump, etc.
medium impact or medium inertia force 1.2 ~ 1.8 vehicle, power machinery, crane, paper machine, etc Metallurgical machinery, concentrators, hoists, machine tools, etc.
strong impact 1.8-3.0 crushers, rolling mills, drilling machines, vibrating screens, etc. in table 9-7, e is the influence coefficient or discriminant coefficient of axial load:
at that time, it means that the influence of axial load is greater, and the effect that must be considered when calculating the equivalent dynamic load is:
= (+)
at that time, In this case:
= note:
1. In formula 9-7, it is the radial load on the bearing, which is usually the vector sum of the radial reaction on the horizontal plane and the radial reaction on the vertical plane of the bearing
2. For deep groove ball bearings, the axial load is determined by the external axial force acting on the shaft. The axial force of the bearing pointed to is the external axial force acting on the shaft (=), and the axial force of the other bearing is zero; For angular contact ball bearings and tapered roller bearings, the axial force is derived from the equilibrium condition between the total axial force and the derived axial force s proced by the radial load
calculation of axial load of four or angular contact ball bearings and tapered roller bearings
when angular contact ball bearings and tapered roller bearings are subjected to pure radial load, the derived axial force will be generated. Figure 9-7 shows the situation of the derived axial force generated by pure radial load when two different installation methods are adopted. Where:
A) is formal (or & quot; Face to face & quot; In this way, the center of the fulcrum can be close to (Fig. 9-8a)
b) is reverse (or & quot; Back to back & quot; The distance between the center of fulcrum is longer (Fig. 9-8b)
with different installation methods, the direction of the derived axial force is also different, but its direction is always from the midpoint of the bearing width to the load center a) Fig. 9-8 analysis of axial load of angular contact ball bearing the derived axial force of angular contact ball bearing and tapered roller bearing shall be calculated according to table 9-9. However, when calculating the reaction force, if the distance between the two bearing fulcrums is not very small, for the sake of simplicity, the midpoint of the bearing width can be used as the action point of the reaction force, so the error is small. Table 9-9 calculation formula of the derived axial force s when about half of the rolling element contacts tapered roller bearings angular contact ball bearings
70000C (a = 15 °) 70000AC(a =25 °) 70000B(a =40 °)
s = FR / (2Y) ① s = 0.5fr, s = 0.7fr, s = 1.1fr note: ① y is corresponding to fa / FR & gt in table 9-7; The value of Y at E
figure 9-9 shows a pair of centripetal angular contact bearings (which can be angular contact ball bearings or tapered roller bearings), and the radial load and axial load acting on the shaft respectively. The radial loads on the two bearings are and, and the corresponding derived axial forces are and. Figure 9-9 axial load of radial angular contact bearing: take the shaft and inner ring of bearing as separation body, when the shaft is in balance, it should meet the following requirements:
+ =
If + & gt;, As shown in Figure 9-10, the shaft tends to move to the right, and the right bearing II is & quot; Press & quot;, The left bearing I is & quot; Relax;. But the axis doesn't actually move. Therefore, according to the balance relationship of forces, the force acting on the outer ring of bearing II should be ＋ & # 39;, And there are:
+ = +, # 39
so
& 39; = + - Figure 9-10 axial force diagram (S1 + fa & gt; The total axial force acting on bearing II is:
= +, # 39; =+ 9-8a)
the axial force acting on bearing I is (that is, bearing 1 is only subjected to its own derived axial force):
= (9-8b)
If + & lt See Figure 9-11). At this time, the shaft tends to move to the left, and bearing I is & quot; Press & quot;, Bearing II is & quot; Relax;, In order to keep the balance of the shaft, there must be a balance force on the outer ring of bearing I; According to the same analysis as above, the axial forces acting on bearing I and bearing II are shown in Fig. 9-11 (S1 + fa & lt; In conclusion, the method of calculating the axial force on angular contact ball bearings and tapered roller bearings can be summarized as follows:
(1) according to the installation mode and type of bearings, determine the direction and size of the derived axial force of bearings
(2) determine the direction and magnitude of the axial external load on the shaft (that is, the algebraic sum of all external axial loads)
(3) determine the direction of the resultant force of all axial loads on the shaft (including the external load and the derived axial load of the bearing); According to the installation form of the bearing, find out the & quot; Compaction & quot; The bearing and by & quot; Relax & quot; The bearing of the bearing
(4) be & quot; Compaction & quot; The axial load of a bearing is equal to the algebraic sum of all other axial loads except the derived axial load itself (that is, the algebraic sum of the derived axial load of another bearing and the external load)
(5) be & quot; Relax & quot; The axial load of the bearing is equal to the derived axial load of the bearing itself 2 If the rotation speed of limit speed check rolling bearing is too high, high temperature will be proced between the friction surfaces, which will affect the performance of lubricant and damage the oil film, resulting in the tempering of rolling element or the failure of component gluing. Therefore, for high-speed rolling bearing, in addition to the fatigue life constraint, it should also meet the speed constraint, the constraint condition is
where: is the maximum working speed of rolling bearing
is the limit speed of rolling bearing. The limit speed value of rolling bearing has been listed in the bearing samples and can be found in relevant standards and manuals. But this speed refers to the maximum allowable speed when the load is not too large (P ≤ 0.1C, C is the basic rated dynamic load), the cooling condition is normal, and the bearing tolerance level is 0. When the bearing is under heavy load
for a single rolling bearing, the so-called NSK bearing life refers to the number of revolutions that one ring can run relative to another ring before fatigue pitting of one ring or rolling element material for the first time
since the fatigue life of rolling bearings is quite discrete under the same working conditions for the same batch of bearings (identical structure, size, material, heat treatment and processing, etc.), the basic rated life can only be used as the standard for selecting bearings
Basic rated life: refers to the total number of revolutions (in revolutions) of a batch of NTN bearings that can operate under the same conditions, of which 90% can operate before fatigue pitting occurs, or the total working hours at a certain speed
Basic rated dynamic load C: the load value that the bearing can bear when the basic rated life of the bearing is 60 rpm. The basic rated dynamic load, for radial fag bearing, refers to the pure radial load, which is also called the radial basic rated dynamic load, expressed in; For the thrust bearing, it refers to the pure axial load, which is also called the axial basic rated dynamic load, expressed in; Diagonal contact ball bearing or tapered roller bearing refers to the radial component of the load which only proces pure radial displacement between the rings
different types of bearings have different basic dynamic load ratings, which represent the bearing capacity of different types of bearings. 2、 Figure 9-7 load life curve of Nachi bearing figure 9-7 is the load life curve of bearing, which shows the relationship between load P and basic rated life. The curve is expressed as:
(rotation) (9-1)
where p is the equivalent dynamic load (n)< br /> ε Is the life index for ball bearings ε ＝ 3 For roller bearings ε ＝ 10/3 In actual calculation, the commonly used hours to represent the bearing life are:
(H) (9-2)
where n is the rotational speed of INA Bearing (R / min)
the change of temperature usually has an impact on the material of bearing elements, the hardness of bearing will be reced, and the bearing capacity will be reced. Therefore, it is necessary to introce the temperature coefficient ft (see table 9-5) to modify the life calculation formula:
(rotation) (9-3)
(H) (9-4) table 9-5 temperature coefficient ft bearing working temperature (℃) ≤ 120 125 150 175 200 225 250 300 350
temperature coefficient ft 1.00 0.95 0.90 0.85 0.80 0.75 0.70 0.60.5 the constraint condition for fatigue life check calculation is
'
where: 39; The predicted life of Koyo bearing is listed in table 9-6 for reference
if the equivalent dynamic load P and speed n are known, the expected calculated life is 39; If it has also been selected, the basic dynamic load rating of the bearing can be calculated from formula (9-5) (?) 39; Value, so that the; Value: select the type of bearing required:
(9-5) Timken bearing expected calculated life recommended in table 9-6 machine type expected calculated life (H)
infrequently used instruments or equipment, such as gate opening and closing device, 300-3000
short-term or intermittent use of machinery, interruption of use will not cause serious consequences, such as manual machinery, 3000-8000
intermittent use of machinery, The consequences of interruption are serious, such as engine aided design, automatic transmission device of flow line, long-distance landing machine, workshop crane, rarely used machine tools and so on, which are 8000-12000
working 8 hours a day (the utilization rate is high), such as general gear drive, some fixed motors and so on, which are 12000-20000
working 8 hours a day (the utilization rate is not high), Such as metal cutting machine tools, continuous use cranes, wood processing machinery, printing machinery and other 20000-30000
24-hour continuous working machinery, such as mine lifts, textile machinery, pumps, motors and other 40000-60000
24-hour continuous working machinery, the consequences of interruption are serious. Such as fiber proction or papermaking equipment, power station main motor, mine water pump, ship propeller shaft, etc.
III. equivalent dynamic load of rolling bearing
Basic rated dynamic load of rolling IKO bearing for radial bearing, it refers to the radial load when the inner ring rotates and the outer ring is stationary, and for radial thrust bearing, it is the radial component of the load that makes the half ring of raceway loaded. For thrust bearings, the basic dynamic load rating is the central axial load. Therefore, the actual working load must be converted into equivalent dynamic load which is the same as the basic rated dynamic load condition before calculation. The equivalent dynamic load after conversion is an imaginary load, which is expressed by symbol. The bearing life under the action of equivalent dynamic load is equal to that under the action of actual load. Under the action of constant radial and axial loads, the calculation formula of equivalent dynamic load is:
(9-6a)
where: is the radial load (n) of the bearing, that is, the radial component of the actual load of the bearing
is the axial load (n) of the bearing, which is the axial component of the actual load of the bearing
is the radial load coefficient, which is the correction coefficient for converting the actual radial load into equivalent dynamic load, as shown in table 9-7
is the axial load factor, which is the correction factor for converting the actual axial load into equivalent dynamic load, as shown in table 9-7
for the radial cylindrical roller bearing, needle roller bearing and spiral roller bearing which can only bear the pure radial load:
= (9-6b)
for the thrust bearing which can only bear the pure axial load:
= (9-6c)
according to the actual working condition of the bearing, the load factor (table 9-8) should be introced to modify it, The modified equivalent dynamic load should be calculated according to the following formula:
= (+) (9-7a)
= (9-7b)
= (9-7c) table 9-8 load coefficient F P load property F P example
no impact or slight impact 1.0 ~ 1.2 motor, steam turbine, fan, water pump, etc.
medium impact or medium inertia force 1.2 ~ 1.8 vehicle, power machinery, crane, paper machine, etc Metallurgical machinery, concentrators, hoists, machine tools, etc.
strong impact 1.8-3.0 crushers, rolling mills, drilling machines, vibrating screens, etc. in table 9-7, e is the influence coefficient or discriminant coefficient of axial load:
at that time, it means that the influence of axial load is greater, and the effect that must be considered when calculating the equivalent dynamic load is:
= (+)
at that time, In this case:
= note:
1. In formula 9-7, it is the radial load on the bearing, which is usually the vector sum of the radial reaction on the horizontal plane and the radial reaction on the vertical plane of the bearing
2. For deep groove ball bearings, the axial load is determined by the external axial force acting on the shaft. The axial force of the bearing pointed to is the external axial force acting on the shaft (=), and the axial force of the other bearing is zero; For angular contact ball bearings and tapered roller bearings, the axial force is derived from the equilibrium condition between the total axial force and the derived axial force s proced by the radial load
calculation of axial load of four or angular contact ball bearings and tapered roller bearings
when angular contact ball bearings and tapered roller bearings are subjected to pure radial load, the derived axial force will be generated. Figure 9-7 shows the situation of the derived axial force generated by pure radial load when two different installation methods are adopted. Where:
A) is formal (or & quot; Face to face & quot; In this way, the center of the fulcrum can be close to (Fig. 9-8a)
b) is reverse (or & quot; Back to back & quot; The distance between the center of fulcrum is longer (Fig. 9-8b)
with different installation methods, the direction of the derived axial force is also different, but its direction is always from the midpoint of the bearing width to the load center a) Fig. 9-8 analysis of axial load of angular contact ball bearing the derived axial force of angular contact ball bearing and tapered roller bearing shall be calculated according to table 9-9. However, when calculating the reaction force, if the distance between the two bearing fulcrums is not very small, for the sake of simplicity, the midpoint of the bearing width can be used as the action point of the reaction force, so the error is small. Table 9-9 calculation formula of the derived axial force s when about half of the rolling element contacts tapered roller bearings angular contact ball bearings
70000C (a = 15 °) 70000AC(a =25 °) 70000B(a =40 °)
s = FR / (2Y) ① s = 0.5fr, s = 0.7fr, s = 1.1fr note: ① y is corresponding to fa / FR & gt in table 9-7; The value of Y at E
figure 9-9 shows a pair of centripetal angular contact bearings (which can be angular contact ball bearings or tapered roller bearings), and the radial load and axial load acting on the shaft respectively. The radial loads on the two bearings are and, and the corresponding derived axial forces are and. Figure 9-9 axial load of radial angular contact bearing: take the shaft and inner ring of bearing as separation body, when the shaft is in balance, it should meet the following requirements:
+ =
If + & gt;, As shown in Figure 9-10, the shaft tends to move to the right, and the right bearing II is & quot; Press & quot;, The left bearing I is & quot; Relax;. But the axis doesn't actually move. Therefore, according to the balance relationship of forces, the force acting on the outer ring of bearing II should be ＋ & # 39;, And there are:
+ = +, # 39
so
& 39; = + - Figure 9-10 axial force diagram (S1 + fa & gt; The total axial force acting on bearing II is:
= +, # 39; =+ 9-8a)
the axial force acting on bearing I is (that is, bearing 1 is only subjected to its own derived axial force):
= (9-8b)
If + & lt See Figure 9-11). At this time, the shaft tends to move to the left, and bearing I is & quot; Press & quot;, Bearing II is & quot; Relax;, In order to keep the balance of the shaft, there must be a balance force on the outer ring of bearing I; According to the same analysis as above, the axial forces acting on bearing I and bearing II are shown in Fig. 9-11 (S1 + fa & lt; In conclusion, the method of calculating the axial force on angular contact ball bearings and tapered roller bearings can be summarized as follows:
(1) according to the installation mode and type of bearings, determine the direction and size of the derived axial force of bearings
(2) determine the direction and magnitude of the axial external load on the shaft (that is, the algebraic sum of all external axial loads)
(3) determine the direction of the resultant force of all axial loads on the shaft (including the external load and the derived axial load of the bearing); According to the installation form of the bearing, find out the & quot; Compaction & quot; The bearing and by & quot; Relax & quot; The bearing of the bearing
(4) be & quot; Compaction & quot; The axial load of a bearing is equal to the algebraic sum of all other axial loads except the derived axial load itself (that is, the algebraic sum of the derived axial load of another bearing and the external load)
(5) be & quot; Relax & quot; The axial load of the bearing is equal to the derived axial load of the bearing itself 2 If the rotation speed of limit speed check rolling bearing is too high, high temperature will be proced between the friction surfaces, which will affect the performance of lubricant and damage the oil film, resulting in the tempering of rolling element or the failure of component gluing. Therefore, for high-speed rolling bearing, in addition to the fatigue life constraint, it should also meet the speed constraint, the constraint condition is
where: is the maximum working speed of rolling bearing
is the limit speed of rolling bearing. The limit speed value of rolling bearing has been listed in the bearing samples and can be found in relevant standards and manuals. But this speed refers to the maximum allowable speed when the load is not too large (P ≤ 0.1C, C is the basic rated dynamic load), the cooling condition is normal, and the bearing tolerance level is 0. When the bearing is under heavy load
6. The deep groove ball bearing does not proce the derived axial force
7. The load capacity of the bearing is closely related to its working conditions. Under the static condition, the thrust ball bearing 8203 can reach 22.2kn, but its rated dynamic load is only 13.5kn; The rated dynamic load of 8206 is only 22kn.
8. Figure
17-7
2.
the acting point of bearing force on the shaft
the fulcrum on the shaft is on the intersection of the normal line of the contact point between the rolling element and the raceway and the axis, as shown in figure
17-8
. In the figure,
o
,
the distance from the outer end face is
a
, which can be found in the manual< br />
" 7"< The
o
points of the bearing are shown in the figure
17-8
<
figure
17-8
3.
calculation of axial force
to analyze the axial load of angular contact bearing, the additional axial force caused by radial force and other working axial forces acting on the shaft should be considered at the same time, and the calculation should be carried out according to the force balance relationship according to the specific situation< In the figure
17-9
,
F
R
and
F
a
are the radial and axial loads acting on the shaft respectively. The radial reactions of the two bearings are
F
R1
and
F
R2
, and the corresponding additional axial forces are
F
S1
and
F
S2
. The axial forces acting on the shaft are shown in
figure
17-10
<
figure
17-9
figure
17-10
according to the balance relationship of the shaft, the axial force on bearing I and II is analyzed according to the following two conditions:
-
If
F
S1
+ F
a
& gt; F
S2
(Fig.
17-11
), the shaft tends to move to the right, making bearing II
& quot
press
& quot
, the right end of the shaft will be subjected to a balance reaction force through the bearing II
F
S2
& 39< From this, the axial force of bearing II can be calculated as
F
A2
= f
S2
+ F
S2
& #= F
S1
+ F
a
because bearing I is only subjected to additional axial force,
F
A1
= f
S1
-
If
F
S1
+ fa & lt; F
S2
(Fig.
17-12
), the shaft tends to move to the left, making bearing I
& quot
press
& quot
, at this time, the left end of
shaft will be subjected to a balance reaction force through bearing I
F
S1
& 39< The axial forces on the two bearings can be calculated as
F
A1
= f
S1
+ F
S1
, respectively= F
S2
- f
a
F
A2
= f
S2
the method of calculating the axial force of angular contact bearing can be summarized as follows:
1
) determine the direction of the resultant force of all axial forces on the shaft (including the external load
and the additional axial force of the bearing), and determine
& quot
press
& quot
end bearing< br />2
"
press
& quot< The
axial force of the end bearing is equal to the algebraic sum of all axial forces except its own additional axial force< The axial force of the bearing at the other end is equal to its own additional axial force
5
calculation formula of static load and limit speed
1
. Static load calculation
static load refers to the load acting on the bearing when the relative speed of bearing ring is zero. In order to limit the excessive contact stress and permanent deformation of rolling bearing under static load, static load calculation is needed. The basic formula of selecting bearing according to rated
static load is
C
0
≥ C
0
& 39= S
0
P
0
where
C
0
-
Basic rated static load,
n
< br />C
0
'-
calculate the rated static load,
n
P
0
-
equivalent static load,
n
s
0
-
safety factor
for static bearing, slow swing bearing or bearing with extremely low speed, the safety factor can be selected according to table
17-9
the safety factor of rotating bearing
s
0
can refer to table
17-10
. If the rotation speed of the bearing is low and the requirements for the running accuracy and friction torque are not high,
s
0
& lt; 1
The thrust self-aligning roller bearing should be taken as
s
0
≥ 4
regardless of rotation
Table
17-9
safety factor of bearing static load
S0
(stationary or swinging)
Table
17-10
safety factor of rotating bearing
S0
2
. When the limit speed of rolling bearing is too high, it will cause high temperature between friction surfaces, affect lubricant performance and damage oil film, From
to
causes the rolling element tempering or component gluing failure
the limit speed of rolling bearing
N0
refers to the speed value when the bearing reaches the maximum thermal equilibrium temperature under certain working conditions. The working speed of the bearing should be lower than its limit speed< The limit speed values given in the performance table of rolling bearing are determined under grease lubrication and oil lubrication conditions respectively,
and are only applicable to
0
grade tolerance, normal lubrication and cooling, fit with rigid bearing seat and shaft, bearing load
p ≤ 0.1C
(
C
is the basic rated dynamic load of bearing, radial bearing is only subject to radial load, The thrust bearing is only subjected to the axial load
when the rolling bearing load
P & gt; When 0.1C
the contact stress will increase; When the bearing bears the combined load, the loaded rolling
moving body will increase, which will increase the friction between the bearing contact surfaces and make the lubrication state worse. At this time, the limit speed value of pole
should be corrected, and the actual allowable speed value can be calculated as follows:
n = f
1
F
2
n
0
where
n -
actual allowable speed,
R / min
n
0
-
bearing limit speed,
R / min
F
1
-
load factor (Figure
17-13
)
F
2
-
load distribution coefficient (Figure
17-14
)
figure
17-14
17-7
2.
the acting point of bearing force on the shaft
the fulcrum on the shaft is on the intersection of the normal line of the contact point between the rolling element and the raceway and the axis, as shown in figure
17-8
. In the figure,
o
,
the distance from the outer end face is
a
, which can be found in the manual< br />
" 7"< The
o
points of the bearing are shown in the figure
17-8
<
figure
17-8
3.
calculation of axial force
to analyze the axial load of angular contact bearing, the additional axial force caused by radial force and other working axial forces acting on the shaft should be considered at the same time, and the calculation should be carried out according to the force balance relationship according to the specific situation< In the figure
17-9
,
F
R
and
F
a
are the radial and axial loads acting on the shaft respectively. The radial reactions of the two bearings are
F
R1
and
F
R2
, and the corresponding additional axial forces are
F
S1
and
F
S2
. The axial forces acting on the shaft are shown in
figure
17-10
<
figure
17-9
figure
17-10
according to the balance relationship of the shaft, the axial force on bearing I and II is analyzed according to the following two conditions:
-
If
F
S1
+ F
a
& gt; F
S2
(Fig.
17-11
), the shaft tends to move to the right, making bearing II
& quot
press
& quot
, the right end of the shaft will be subjected to a balance reaction force through the bearing II
F
S2
& 39< From this, the axial force of bearing II can be calculated as
F
A2
= f
S2
+ F
S2
& #= F
S1
+ F
a
because bearing I is only subjected to additional axial force,
F
A1
= f
S1
-
If
F
S1
+ fa & lt; F
S2
(Fig.
17-12
), the shaft tends to move to the left, making bearing I
& quot
press
& quot
, at this time, the left end of
shaft will be subjected to a balance reaction force through bearing I
F
S1
& 39< The axial forces on the two bearings can be calculated as
F
A1
= f
S1
+ F
S1
, respectively= F
S2
- f
a
F
A2
= f
S2
the method of calculating the axial force of angular contact bearing can be summarized as follows:
1
) determine the direction of the resultant force of all axial forces on the shaft (including the external load
and the additional axial force of the bearing), and determine
& quot
press
& quot
end bearing< br />2
"
press
& quot< The
axial force of the end bearing is equal to the algebraic sum of all axial forces except its own additional axial force< The axial force of the bearing at the other end is equal to its own additional axial force
5
calculation formula of static load and limit speed
1
. Static load calculation
static load refers to the load acting on the bearing when the relative speed of bearing ring is zero. In order to limit the excessive contact stress and permanent deformation of rolling bearing under static load, static load calculation is needed. The basic formula of selecting bearing according to rated
static load is
C
0
≥ C
0
& 39= S
0
P
0
where
C
0
-
Basic rated static load,
n
< br />C
0
'-
calculate the rated static load,
n
P
0
-
equivalent static load,
n
s
0
-
safety factor
for static bearing, slow swing bearing or bearing with extremely low speed, the safety factor can be selected according to table
17-9
the safety factor of rotating bearing
s
0
can refer to table
17-10
. If the rotation speed of the bearing is low and the requirements for the running accuracy and friction torque are not high,
s
0
& lt; 1
The thrust self-aligning roller bearing should be taken as
s
0
≥ 4
regardless of rotation
Table
17-9
safety factor of bearing static load
S0
(stationary or swinging)
Table
17-10
safety factor of rotating bearing
S0
2
. When the limit speed of rolling bearing is too high, it will cause high temperature between friction surfaces, affect lubricant performance and damage oil film, From
to
causes the rolling element tempering or component gluing failure
the limit speed of rolling bearing
N0
refers to the speed value when the bearing reaches the maximum thermal equilibrium temperature under certain working conditions. The working speed of the bearing should be lower than its limit speed< The limit speed values given in the performance table of rolling bearing are determined under grease lubrication and oil lubrication conditions respectively,
and are only applicable to
0
grade tolerance, normal lubrication and cooling, fit with rigid bearing seat and shaft, bearing load
p ≤ 0.1C
(
C
is the basic rated dynamic load of bearing, radial bearing is only subject to radial load, The thrust bearing is only subjected to the axial load
when the rolling bearing load
P & gt; When 0.1C
the contact stress will increase; When the bearing bears the combined load, the loaded rolling
moving body will increase, which will increase the friction between the bearing contact surfaces and make the lubrication state worse. At this time, the limit speed value of pole
should be corrected, and the actual allowable speed value can be calculated as follows:
n = f
1
F
2
n
0
where
n -
actual allowable speed,
R / min
n
0
-
bearing limit speed,
R / min
F
1
-
load factor (Figure
17-13
)
F
2
-
load distribution coefficient (Figure
17-14
)
figure
17-14
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