Abstract
Gears are toothed wheels that are widely used for power and motion transmission between rotating shafts. Based on the relative position of the shafts, gear drives can be fell into three principal categories, namely parallel-shaft gear drives, intersecting-shaft gear drives, and crossed gear drives. Parallel-shaft gear drives are the most common type of drives, because they are simples. Among them, spur gears and helical gears are more popular. This chapter deals with designing spur and helical gear drives. Gearings design requires using complex diagrams and many trials and errors. However, in this chapter, we propose methods that give very good approximations and easy calculations for the design.
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Abbreviations
- a :
-
Center distance, mm
- b :
-
Teeth face width (gear width), mm
- \(D_G\) :
-
Pitch circle diameter of gear, mm
- \(D_p\) :
-
Pitch circle diameter of pinion, mm
- d :
-
Shaft diameter, mm
- \(H_G\) :
-
Gear hardness
- \(H_p\) :
-
Pinion hardness
- HB :
-
Brinell hardness scale
- HRB :
-
Rockwell hardness scale B
- HRC :
-
Rockwell hardness scale C
- HV :
-
Vickers hardness scale
- \(\begin{aligned} & k, \\ & k_0 - k_5 , \\ & k_A , \\ & k_{H\beta } \\ \end{aligned}\) :
-
Factors for the equations
- m :
-
Module, transverse module of helical gears, mm
- \(m_n\) :
-
Normal module, mm
- \(n_G\) :
-
Rotational speed of gear, rpm
- \(n_p\) :
-
Rotational speed of pinion, rpm
- T :
-
Torque, N m
- \(T_1\) :
-
Torque on the shaft of pinion, N m
- \(T_E\) :
-
Maximum torque of engine, N m
- u :
-
Speed ratio, transmission ratio
- \(\begin{aligned} & u_1 , u_2 , \\ & and\,u_3 \\ \end{aligned}\) :
-
Transmission ratios of gear stages in a multi-stage gearbox
- \(u_t\) :
-
Overall transmission ratio of a multi-stage gearbox
- \(z_G\) :
-
Number of gear teeth
- \(z_p\) :
-
Number of pinion teeth
- β :
-
Helix angle, degrees
- \(\sigma_F\) :
-
Allowable bending stress, MPa
- \(\sigma_H\) :
-
Allowable contact stress, MPa
- φ :
-
Ratio of pinion width to its pitch circle diameter
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Yaghoubi, M., Tavakoli, H. (2022). Spur and Helical Gear Drives. In: Mechanical Design of Machine Elements by Graphical Methods. Materials Forming, Machining and Tribology. Springer, Cham. https://doi.org/10.1007/978-3-031-04329-1_19
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DOI: https://doi.org/10.1007/978-3-031-04329-1_19
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