CB* 3299-1987 Calculation method for load-bearing capacity of involute cylindrical gears for ships
Some standard content:
National Ship Standardization Technical Committee Professional Standard CB*3299--87
Ship Involute Gear
Carrying Capacity Calculation Method
Published on 1987-02-01
National Ship Standardization Technical Committee
Implemented on 1987-12-01
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Calculation Method
CB*3299--87
Classification Number: U48
This standard is applicable to the main drive steel involute spur, helical and herringbone gear transmission of ships. Other ship transmission gears can also be used for reference.
This standard includes two verification calculation methods for tooth surface contact strength and gear tooth bending strength. General Principles and General Coefficients
1.1 Related Standards
This standard is formulated based on the basic method of GB3480-83 "Calculation Method for Load Capacity of Involute Cylindrical Gears". The tooth profile used in this standard shall comply with the provisions of GB1356-78 "Benchmark Tooth Profile of Involute Cylindrical Gears". The gear accuracy standard corresponding to this standard is JB179-83 "Involute Cylindrical Gear Accuracy". 1.2 Text Symbols
The commonly used text symbols in this standard are shown in Table 1. Table" Commonly used text symbols
di, d2
dsl, da2
dbl, db2
d, d2
Center distance, center distance of standard gear and highly modified gearCenter distance of angular modified gear
Calculated tooth width
Half of the tooth width of herringbone gear
Node, coefficient
Tooth tip relief (measured along the normal direction of the tooth profile)Tooth tip relief caused by running-in
Meshing stiffness
Measurement of a single pair of teeth
Pitch circle diameter of small wheel and large wheel
Tooth of small wheel and large wheel Top circle diameter
Base circle diameter of small wheel and large wheel
Root circle diameter of small wheel and large wheel
Elastic modulus (Young's modulus)
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N/mmμm
N/mm'um
1987-12-01 Implementation
ni, n2
CB*3299-87
Continued Table 1
On the inner dividing circle of the end face Nominal tangential force tooth tolerance
Initial meshing tooth error
Meshing tooth error after running-in
Tooth shape tolerance
Base pitch limit deviation
Brinell hardness
Rockwell hardness
Vickers hardness at F=9.8N
Vickers hardness at F=98.1N
Tooth top height
Bending force arm when load acts on the upper boundary point of the meshing area of a single pair of teethTool basic tooth profileTooth top height
Use coefficient
Tooth load distribution coefficient for bending strength calculationTooth load distribution coefficient for bending strength calculationContact Inter-tooth load distribution coefficient for strength calculationTooth load distribution coefficient for contact strength calculationDynamic load coefficient
Moduli; equivalent mass
Normal modulus
Induced mass
End modulus
Critical speed ratio; index
Number of stress cycles
Speeds of small and large wheels
Critical speed of small wheels
Normal base
End base
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mm; kg/mm
min -!
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T1, T2
XI, X2
YRrelT
Ysrelt
Auxiliary coefficient
CB*3299-87
Continued Table 1
Unit tooth width flexibility
Tooth root fillet parameters
Arithmetic mean of roughness|| tt||Average roughness
Radius, pitch circle radius
Calculated safety factor for bending strength
Minimum safety factor for bending strength
Calculated safety factor for contact strength
Minimum safety factor for contact strength
Tooth thickness; size
Chordal tooth thickness on dangerous section
Nominal torque of small wheel and large wheel
Tooth ratio μ=z/z,>1||t t||Linear speed; circumferential speed of pitch circle
Normal displacement coefficient of small wheel and large wheel
Tooth shape coefficient when load acts on the upper boundary point of meshing area of single pair of teethCompound tooth shape coefficient when load acts on tooth topLife coefficient for bending strength calculation
Relative tooth root surface condition coefficient
Stress correction coefficient when load acts on the upper boundary point of meshing area of single pair of teethStress correction coefficient for test gear
Dimension coefficient for bending strength calculation
Helix angle coefficient for bending strength calculation
Relative tooth root fillet sensitivity coefficient
Tooth run-in
Tooth run-in
Lower boundary point coefficient
Elastic coefficient
Node area coefficient
Lubricant coefficient
Life coefficient for contact strength calculation
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VN/mm?
Z1, z2
Zal, Za2
Roughness coefficient
Speed coefficient
CB*3299—87
Continued Table 1
Tooth surface working hardening coefficient
Size coefficient for contact strength calculation||tt| |Helix angle coefficient for contact strength calculation
Contact coefficient for contact strength calculation
Number of teeth of small wheel and large wheel
Equivalent number of teeth of small wheel and large wheel of helical gearNormal pitch circle pressure angle
End pitch circle pressure angle
End face meshing angle
Pitch circle helix angle
Base circle helix angle
End face overlap
Longitudinal overlap
Total overlap
Moment of inertia of small and large wheels
Kinematic viscosity of lubricating oil
Poisson's ratio
Radius of curvature
Radius of fillet of basic rack tooth tip
Equivalent radius
Radius of curvature at node
Tensile strength
Calculation of tooth root stress
Basic value of calculation of tooth root stress
Allowable tooth root stress
Bending fatigue limit of test gear Limit
Calculation of contact stress
Basic value of calculated contact stress
Allowable contact stress
Contact fatigue limit of test gear
1.3 Scope of application of graphs, formulas and constants 1.3.1 Life
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', rad
, rad
o, rad
, rad
e, rad
kgimm2
kg/mml
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This standard calculates the endurance life strength of gears according to the actual operating conditions or commonly used operating conditions of marine main transmission cylindrical gears. The endurance life usually refers to the number of tooth surface contact stress cycles N>5×107 times, and the number of gear tooth bending stress cycles NL>3×10° times. At this time, the life coefficient Zn for contact strength calculation is taken as 1, and the life coefficient YNT for bending strength calculation is taken as 1. If a large short-term overload occurs during use, the contact strength and bending strength of the gear should also be calculated for static strength according to Article 3.20 of GB3480-83. 1.3.2 Structure
Each gear must be arranged between bearings (related to KH, KF). 1.3.3 Speed range
Linear speed,>1m/s (because speed is related to wear, when the circumferential speed is lower than 1m/s, the gear's load-bearing capacity is mainly limited by the allowable tooth surface wear and cold bonding).
1.3.4 Gear accuracy
Gear accuracy grade shall not be lower than Grade 7 of JB179-83. 1.3.5 Surface roughness of tooth root fillet
The average roughness of tooth root fillet surface Rz<16um, and all processing marks such as scratches, knife marks, grinding or shaving steps shall be repaired to make the tooth root fillet smooth transition (in this case, YrrelT=1). 1.3.6 End face overlap
8aa<2.0 (related to Y.)
1.3.7 Materials
Civilian ships shall be selected in accordance with the relevant provisions of Chapter 5 of Part 8 of the "Rules for Classification and Construction of Steel Seagoing Vessels 1983" of the Ship Inspection Bureau of the People's Republic of China, and military ships shall be selected in accordance with the relevant provisions of Section 5 of Chapter 7 of the "Rules for Ship Construction". All processed gear forgings with a diameter exceeding 200mm shall be subjected to ultrasonic flaw detection on the surface of the cutting part. All surface hardened gear teeth shall be subjected to magnetic particle flaw detection or color inspection. For the gear teeth of non-surface hardened forged gears, the above inspection should also be carried out after finishing.
1.4 Treatment methods for situations beyond the scope of application of diagrams, formulas and constants If the use situation exceeds the scope of application specified by the diagrams, tables, formulas and constants of this standard, and no other standards are available, the following methods can be used.
8. Various coefficients can be determined according to the rules of diagrams, tables, formulas and constants. Generally speaking, if the diagrams and formulas are outside the scope of use, they should be calculated in accordance with GB3480-83.
b. If reliable empirical data or test data can be provided for each influencing parameter, then these data can be used instead of the coefficients given in this standard, but the reliability of the data must be stated in the calculation results. 1.5 Nominal tangential force F
The nominal tangential force acts on the end face and cuts the pitch circle, and is determined by the nominal power transmitted by the gear pair. The nominal tangential force can be calculated according to formula (1): d1, 27
Tl, 2
F=2000T,
di, 2
-small and large gear pitch circle diameter, mm; small and large gear nominal torque, N·m. The nominal torque of the gear is calculated according to formula (2):
T1, 2 = 9549
nj, 2
-power, kW;
-where: P
1, 2-
-speed of the small wheel and the large wheel, min-\
The nominal torque used in this standard is the torque transmitted during long-term operation under the maximum load condition, which is usually set as the rated torque of the engine. For short-term overload conditions, see Section 1.3.1.
1.6 Reliability and safety factor
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When designing gears, reliability requirements should be taken into account. The reliability requirements of gear operation are determined by comprehensive consideration of factors such as its importance, working requirements and maintenance difficulty. Marine gears are required to have high reliability over a long service life. The reliability requirement is generally not less than 99% (the probability of failure is less than 1%). The high reliability requirement is not less than 99.9% (the probability of failure is less than 0.1%). Considering that there is a certain deviation between the calculation results and the actual situation, in order to ensure the required reliability Reliability must ensure that the calculated allowable load-bearing capacity has the necessary safety margin. Obviously, the more accurate the calculation method, the smaller the deviation from the actual situation, the smaller the required safety margin can be, and the more unified the economy and reliability.
When selecting the specific safety factor, the following points must be noted: a. The fatigue limit recommended by this standard is obtained when the probability of gear failure is 1%. The safety factor should be selected based on reliability requirements, operating conditions and practical experience. This standard recommends the following minimum safety factors: The minimum safety factor for contact strength SHmia is generally: SHmin=1.10 (failure probability less than 1%) SHmia=1.30 (failure probability less than 0.1%) The specific value of the minimum safety factor is recommended to be determined by the user and the manufacturer. Due to broken teeth The damage has more serious consequences than pitting damage, so when designing gears, the safety factor of bending strength should be greater than the safety factor of contact strength. Hardened gears require a larger safety factor. b. The minimum safety factors SHmin and SFmin are only applicable when all influencing factors have been mastered and remain basically unchanged during operation. These influencing factors include: load, manufacturing deviation, material and heat treatment quality, assembly and installation accuracy, connection between the prime mover and the working machine, lubrication, use, safety and control devices, etc. The closer these factors are to reality, the smaller the safety factor can be, otherwise it should be larger.
1.7 Order of calculation of coefficients
Each load coefficient is related to the tangential force on the inner pitch circle of its corresponding end face. Therefore, the calculations should be made in the following order: b. use F.·KA to find Kv;
b. use F.·KA·Kv to find KHB (KFB);
c. use F·KA·Kv·KH to find KHa (KFa). 1.8 Use factor KA
The use factor K^ is a factor that takes into account the influence of dynamic overload caused by external factors of meshing. This overload depends on the characteristics, mass ratio, coupling type and operating status of the prime mover and driven machinery. The transmission designer should conduct a comprehensive dynamic analysis of the entire system and monitor the working conditions of the shaft system during the sea trial to ensure that the transmission is not subject to vibration caused by excessive periodic loads. When conducting a dynamic analysis, it is necessary to master the factors such as the mass, stiffness and damping of the transmission system. When there is no credible experience or reliable load spectrum, KA is obtained according to Table 2.
If the load spectrum is known, the equivalent torque Tred obtained from the load spectrum can be used to replace T·KA for calculation. Table 2 Service factor KA
Gas turbine, steam turbine, hydraulic,
Electric or other stable drive
Any type of prime mover
Number of cylinders
Primary mover and gear box
Coupling form
Any form
Hydraulic coupling, high elastic coupling
Or other suction coupling
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Four-stroke diesel engine
Two-stroke diesel engine
CB*3299-—87
Continued Table 2
Between prime mover and gear box
Coupling type
Elastic coupling
Rigid coupling
Elastic coupling
Rigid coupling
71.411.30
Note: When the propeller is rigidly connected to the diesel engine, the torque variation caused by the above values may be 15%. 1.9 Dynamic load coefficient Kv
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The dynamic load coefficient Kv is a coefficient used to consider the internal dynamic overload caused by the meshing vibration of the large and small gears. Kv is defined as the ratio of the actual maximum force when the gear pair is meshing to the corresponding force generated purely by the external load. The main factors affecting the dynamic load coefficient are:
Transmission error caused by base pitch and tooth profile error; a.
Mass (moment of inertia) of large and small wheels and corresponding rotating parts; meshing stiffness, especially the change of stiffness in the gear meshing cycle; the magnitude of the tangential force after considering KA;
Speed and pitch line speed;
Lubrication conditions;
Damping characteristics of the gear system;
Stiffness of the shaft and bearings;
Contact conditions on the load-bearing tooth surface.
If the maximum tangential load including the internal dynamic load can be determined by actual measurement or comprehensive dynamic analysis of all influencing factors, Kv=1 can be taken, but at this time, the accuracy and reliability of the method adopted must be demonstrated, and the prerequisites must be clearly given. When the above requirements are difficult to achieve, the dynamic load coefficient can be calculated using the method provided in this standard. 1.9.1 Critical speed ratio N
The simplified gear meshing vibration model has a critical speed n1. The ratio N of the small wheel speed m to the critical speed nei is called the critical speed ratio.
The critical speed ratio N is calculated according to formula (3):
Where: z1
Number of small gear teeth;
30-103
C, gear meshing stiffness, N/mmum (see 1.12.1); mred--induced mass; kg/mm, calculated by formula (4): mred
Where: m1, m2 represent the equivalent mass per unit tooth width of the small wheel and the large wheel converted to the meshing line, kg/mm. m; and m2 are calculated by formula (5):
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CB*3299-87
In the formula: ?1, ?2—rotational inertia of small wheel and large wheel, kg·mm\; b—tooth width, mm, here should take the actual size of each; rbr, rb—base circle radius of small wheel and large wheel, mm. For general transmission, the induced mass mred of gear pair can be approximately calculated as follows: m red =
Material density, kg/mm\;
In the formula: p
In the formula: D:-
Base circle diameter, mm;
-Average diameter, mm,.
(1-q)p+(1-q)p2 u2
(d+dr)
Inner cavity diameter of the outer gear rim,
, mm.
Where: Do—diameter of the outer circle of the internal gear; mm. The meaning of the above diameters can be found in Figure 1.
, for external gears
; for internal gears
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Figure 1 Gear diameters
In formula (6), for web-type and spoke-type gears, the weight of the web, wheel belly, and wheel hub can be ignored. For the small and large wheels of the integral structure, the following can be taken:
That is, q=0
92 = 0
1-f=1,1-=1;
When the ring gear width is different from the tooth width, 1-gi or 1-q2 can be calculated only according to the ring gear, and only the weight directly connected to the ring gear is considered, while the weight far away from the gear on the same shaft can be ignored, because the stiffness of the shaft is mostly lower than that of the gear. The resonant speed of the gear pair consisting of a large wheel and an integral pinion can also be found from Figure 2. o
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CB*3299-87
Figure 2, a line diagram for calculating the critical speed nei of a steel gear pair (the pinion is an integral structure) Free Standard Download Network (www.freebz.net) For planetary transmissions and other special gears, such as the average diameter of the pinion close to its shaft diameter, two rigidly connected coaxial gears, two pinions driving a large gear, etc., the induced weight can be approximately calculated according to the formulas in Table 3.3-1 and Table 3.3-2 of CB3480-83.
1.9.2 Calculation formula of Kv
The critical speed ratio N has an extremely important influence on the dynamic load coefficient of the gear device. When N=1, the operating speed n=nEI, at which time Kv reaches the maximum value. In different N value ranges, that is, different operating speed ranges, the influence of meshing vibration on Kv is different. Taking into account the deviation between the calculation results and the actual situation caused by the simplification of the vibration model and the neglect of minor influencing factors, the operating speed is divided into 4 intervals according to the N value. The corresponding Kv calculation formula is shown in Table 3. Table 3 Calculation formula of operating speed range and dynamic load coefficient Kv Requirements of operating critical speed for operating gears in speed range Most general gears work in this area Calculation formula of Kv Kv=N·K+1=N(Cvi·BP+CvzBr+Cv?Bk Free standard download network (www.freebz.net)) No registration is required to download the preparation When N=1/2 or 1/3, resonance may occur, and Kv greatly exceeds the calculated value, especially for spur gears. At this time, the design should be modified. When N: 1/4 or 1/5, the resonance effect is very small. Requirements for the running gears in the critical speed range. Generally, gears with low precision (especially unrepaired straight gears) should not run in this area. High-precision helical gears with precision>2 can work in this area. Most turbine gears and other high-speed gears are in this area. CB*3299—87 Continued Table 3 Kv calculation formula Kv=Cvi ·Bp+Cv2·Br+Cva·B+1K, (N=1.15) Kv(N-1.5)
Kv=Cv-B,+
Free Standard Download Network (www.freebz.net) Note
K in this area is greatly affected by damping
. The actual dynamic
load and the value calculated
by formula (11) can differ by up to 40%.
Especially for unrepaired straight
Kv(N=1.15) according to (11)
Kv(N=1.5) according to formula (13)
(1) may resonate when V=2
or 3, but
the effect is not significant.
(2) When the lateral vibration natural frequency
of the shaft-gear system is close to or equal to the meshing frequency
of the operation, the actual
dynamic load and the value calculated by formula (13) may differ by
by 100%. This situation should be avoided. In each formula of Table 3, each gear pair is treated as a single-stage transmission, ignoring the influence of other stages in multi-stage transmission. Coaxial gears with non-rigid connection can be simplified in this way. Otherwise, they should be treated according to the second type of situation in Table 3.3-2 of GB3480-83. In the formulas in Table 3: Bp---dimensionless parameter considering the effect of base pitch deviation on dynamic load, its value is calculated according to formula (14): C'fpber
-dimensionless parameter considering the effect of tooth profile error on dynamic load, its value is calculated according to formula (15): Br =C'frerr
dimensionless parameter considering the effect of gear tooth trimming on dynamic load, its value is calculated according to formula (16): c'c
(For gears with accuracy lower than grade 5, Bk=1 should be taken) ..…Free Standard Download Network (www.freebz.net) can be downloaded without registration (14)
(15)2Kv calculation formula
The critical speed ratio N has an extremely important influence on the dynamic load coefficient of the gear device. When N=1, the operating speed n=nEI, at this time Kv reaches the maximum value. In different N value intervals, that is, different operating speed intervals, the influence of meshing vibration on Kv is different. Considering the deviation between the calculation results and the actual situation caused by the simplification of the vibration model and the neglect of minor influencing factors, the operating speed is divided into 4 intervals according to the N value. The corresponding Kv calculation formula is shown in Table 3. Table 3 Calculation formula of operating speed range and dynamic load coefficient Kv Requirements of operating critical speed for operating gears in speed range Most general gears work in this area Calculation formula of Kv Kv=N·K+1=N(Cvi·BP+CvzBr+Cv?Bk Free standard download network (www.freebz.net)) No registration is required to download the preparation When N=1/2 or 1/3, resonance may occur, and Kv greatly exceeds the calculated value, especially for spur gears. At this time, the design should be modified. When N: 1/4 or 1/5, the resonance effect is very small. Requirements for the running gears in the critical speed range. Generally, gears with low precision (especially unrepaired straight gears) should not run in this area. High-precision helical gears with precision>2 can work in this area. Most turbine gears and other high-speed gears are in this area. CB*3299—87 Continued Table 3 Kv calculation formula Kv=Cvi ·Bp+Cv2·Br+Cva·B+1K, (N=1.15) Kv(N-1.5)
Kv=Cv-B,+
Free Standard Download Network (www.freebz.net) Note
K in this area is greatly affected by damping
. The actual dynamic
load and the value calculated
by formula (11) can differ by up to 40%.
Especially for unrepaired straight
Kv(N=1.15) according to (11)
Kv(N=1.5) according to formula (13)
(1) may resonate when V=2
or 3, but
the effect is not significant.
(2) When the lateral vibration natural frequency
of the shaft-gear system is close to or equal to the meshing frequency
of the operation, the actual
dynamic load and the value calculated by formula (13) may differ by
by 100%. This situation should be avoided. In each formula of Table 3, each gear pair is treated as a single-stage transmission, ignoring the influence of other stages in multi-stage transmission. Coaxial gears with non-rigid connection can be simplified in this way. Otherwise, they should be treated according to the second type of situation in Table 3.3-2 of GB3480-83. In the formulas in Table 3: Bp---dimensionless parameter considering the effect of base pitch deviation on dynamic load, its value is calculated according to formula (14): C'fpber
-dimensionless parameter considering the effect of tooth profile error on dynamic load, its value is calculated according to formula (15): Br =C'frerr
dimensionless parameter considering the effect of gear tooth trimming on dynamic load, its value is calculated according to formula (16): c'c
(For gears with accuracy lower than grade 5, Bk=1 should be taken) ..…Free Standard Download Network (www.freebz.net) can be downloaded without registration (14)
(15)2Kv calculation formula
The critical speed ratio N has an extremely important influence on the dynamic load coefficient of the gear device. When N=1, the operating speed n=nEI, at this time Kv reaches the maximum value. In different N value intervals, that is, different operating speed intervals, the influence of meshing vibration on Kv is different. Considering the deviation between the calculation results and the actual situation caused by the simplification of the vibration model and the neglect of minor influencing factors, the operating speed is divided into 4 intervals according to the N value. The corresponding Kv calculation formula is shown in Table 3. Table 3 Calculation formula of operating speed range and dynamic load coefficient Kv Requirements of operating critical speed for operating gears in speed range Most general gears work in this area Calculation formula of Kv Kv=N·K+1=N(Cvi·BP+CvzBr+Cv?Bk Free standard download network (www.freebz.net)) No registration is required to download the preparation When N=1/2 or 1/3, resonance may occur, and Kv greatly exceeds the calculated value, especially for spur gears. At this time, the design should be modified. When N: 1/4 or 1/5, the resonance effect is very small. Requirements for the running gears in the critical speed range. Generally, gears with low precision (especially unrepaired straight gears) should not run in this range. High-precision helical gears with precision>2 can work in this range. Most turbine gears and other high-speed gears are in this range. CB*3299—87 Continued Table 3 Kv calculation formula Kv=Cvi ·Bp+Cv2·Br+Cva·B+1K, (N=1.15) Kv(N-1.5)
Kv=Cv-B,+
Free Standard Download Network (www.freebz.net) Note
K in this area is greatly affected by damping
. The actual dynamic
load and the value calculated
by formula (11) can differ by up to 40%.
Especially for unrepaired straight
Kv(N=1.15) according to (11)
Kv(N=1.5) according to formula (13)
(1) may resonate when V=2
or 3, but
the effect is not significant.
(2) When the lateral vibration natural frequency
of the shaft-gear system is close to or equal to the meshing frequency
of the operation, the actual
dynamic load and the value calculated by formula (13) may differ by
by 100%. This situation should be avoided. In each formula of Table 3, each gear pair is treated as a single-stage transmission, ignoring the influence of other stages in multi-stage transmission. Coaxial gears with non-rigid connection can be simplified in this way. Otherwise, they should be treated according to the second type of situation in Table 3.3-2 of GB3480-83. In the formulas in Table 3: Bp---dimensionless parameter considering the effect of base pitch deviation on dynamic load, its value is calculated according to formula (14): C'fpber
-dimensionless parameter considering the effect of tooth profile error on dynamic load, its value is calculated according to formula (15): Br =C'frerr
dimensionless parameter considering the effect of gear tooth trimming on dynamic load, its value is calculated according to formula (16): c'c
(For gears with accuracy lower than grade 5, Bk=1 should be taken) ..... Free Standard Download Network (www.freebz.net) can be downloaded without registration (14)
(15)
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