For a helical gear with N actual teeth and a helix angle psi, what is the formula for its virtual number of teeth N'?

Correct answer: N' = N / cos^3(psi)

Explanation

The concept of 'virtual number of teeth' is used in helical gear design to analyze the tooth's strength as if it were a spur gear. The formula N' = N / cos^3(psi) calculates the number of teeth on this equivalent spur gear, which has a larger pitch radius due to the helix angle.

Other questions

Question 1

Which type of gear has teeth inclined to the axis of rotation and can be used to transmit motion between both parallel and nonparallel shafts?

Question 2

What is the term for the ratio of the number of teeth on a gear to its pitch diameter, typically expressed in teeth per inch?

Question 3

A gearset consists of a 20-tooth pinion driving a 50-tooth gear. If the diametral pitch is 2.5, what is the center distance between the gears?

Question 4

What is the primary advantage of using involute profiles for gear teeth?

Question 5

What is the smallest number of teeth a full-depth spur pinion can have to run with itself (a one-to-one gear ratio) without interference, if the pressure angle is 20 degrees?

Question 6

A helical gear has a transverse diametral pitch (Pt) of 8 teeth/in and a helix angle (psi) of 30 degrees. What is its normal diametral pitch (Pn)?

Question 7

In a worm gearset with a 90 degree shaft angle, what is the relationship between the axial pitch (px) of the worm and the transverse circular pitch (pt) of the gear?

Question 8

A simple gear train consists of a 20-tooth driving gear, a 50-tooth idler gear, and a 100-tooth driven gear. If the driving gear rotates at 1000 rev/min, what is the speed of the final driven gear?

Question 9

What is the term for the contact of portions of gear tooth profiles that are not conjugate, often occurring when the pinion has too few teeth?

Question 10

A pinion with a pitch diameter of 50 mm runs at 1750 rev/min and transmits 2.5 kW of power. What is the transmitted load (Wt)?

Question 11

A two-stage compound gear train is needed for a 40:1 speed reduction. To minimize package size, what is the ideal gear ratio for each stage?

Question 12

In a compound reverted gear train, what geometric condition must be satisfied in addition to the ratio requirements, assuming a constant diametral pitch?

Question 13

What is the formula for the train value 'e' of a planetary gear train?

Question 14

In the force analysis of a straight-tooth bevel gear, a resultant force W has three components. What are these three components?

Question 15

What is Tredgold's approximation used for in the context of bevel gears?

Question 16

A helical gear has a normal pressure angle (phi_n) of 20 degrees and a helix angle (psi) of 30 degrees. What is its transverse pressure angle (phi_t)?

Question 18

What is the recommended minimum contact ratio for gears to avoid impact between teeth and reduce noise?

Question 19

What is the relationship between circular pitch (p) and diametral pitch (P)?

Question 20

A worm has a lead (L) of 1.0472 inches and a pitch diameter (dW) of 2 inches. What is its lead angle (lambda)?

Question 21

What type of gear is used to transmit motion between intersecting shafts, with teeth formed on conical surfaces?

Question 22

What is the term for the radial distance from the top land of a gear tooth to the pitch circle?

Question 23

A gearset is designed with a 15-tooth pinion and a 60-tooth gear. Both have a 20-degree pressure angle. According to Equation (13-11), what is the smallest number of teeth the pinion could have to avoid interference?

Question 24

What type of gear resembles a screw and is typically used when the speed ratios of the two shafts are quite high, such as 3 or more?

Question 25

A gear has a pitch diameter of 3 inches and rotates at 1800 rev/min. What is its pitch-line velocity (V) in ft/min?

Question 26

In a planetary gear train, the sun gear (first gear) rotates at -100 rev/min (clockwise), the arm rotates at -20 rev/min (clockwise), and the train value is -0.25. What is the speed of the ring gear (last gear)?

Question 27

What is a double helical gear, also known as a herringbone gear, equivalent to?

Question 28

In the context of gear nomenclature, what is the 'pinion'?

Question 29

What is the relationship between the base pitch (pb) and circular pitch (pc) of a spur gear with pressure angle (phi)?

Question 30

A straight-tooth bevel pinion has 15 teeth and drives a 45-tooth gear. What is the pitch angle (gamma) of the pinion?

Question 31

In a helical gear system, a transmitted load (Wt) of 50 lbf is applied. The transverse pressure angle (phi_t) is 22.8 degrees and the helix angle (psi) is 30 degrees. What is the axial thrust load (Wa)?

Question 32

What is the primary reason for using a larger pressure angle, like 25 degrees instead of 20 degrees, in gear design?

Question 33

Which gear manufacturing process involves cutting teeth with a tool shaped like a worm?

Question 34

For a standard 20 degree straight bevel gear, what is the minimum number of teeth recommended for a pinion that mates with a 30-tooth gear?

Question 35

What happens to the pressure angle and the length of the line of action when the center distance of a pair of involute gears is increased?

Question 36

In a simple gear train, the train value 'e' is positive if the last gear rotates in the same sense as the first. This occurs when the number of meshes is what?

Question 37

Which type of gear is patented, has curved teeth, but a zero spiral angle?

Question 38

What is the primary characteristic of hypoid gears that distinguishes them from spiral bevel gears?

Question 39

What is the module (m) of a gear with 50 teeth and a pitch diameter of 125 mm?

Question 40

A gearset transmits 5 hp at a pitch-line velocity of 406 ft/min. What is the transmitted load (Wt) in lbf?

Question 41

What is the general term for tooth profiles designed to produce a constant angular-velocity ratio during meshing?

Question 42

A gear with a module of 3 mm has 60 teeth. What is its pitch diameter?

Question 43

In a planetary gear system shown in Figure 13-26, the sun gear has 20 teeth and the ring gear has 80 teeth. What is the train value 'e' assuming a fixed arm?

Question 44

For an internal gear meshing with a pinion, where is the addendum circle of the internal gear located?

Question 45

In a worm gearset, the efficiency (eta) is given by the formula (cos(phi_n) - f * tan(lambda)) / (cos(phi_n) + f * cot(lambda)). What happens to the efficiency as the lead angle (lambda) increases, assuming f and phi_n are constant?

Question 46

What is the primary purpose of the finishing processes of shaving, burnishing, grinding, or lapping gear teeth?

Question 47

A gearset is being designed with an incorrectly large center distance. What is the effect on the base circles of the two gears?

Question 48

What is the formula for calculating the sliding velocity (VS) in a worm gearset, given the worm pitch-line velocity (VW) and the lead angle (lambda)?

Question 49

A two-stage compound reverted gear train is being designed for an exact 30:1 ratio with a 20 degree pressure angle. The first stage ratio is 6:1. If the smallest pinion (N3) must have at least 16 teeth, what is the smallest integer value for N3 that will result in an integer number of teeth for all gears?

Question 50

What is the primary distinguishing feature of a gear rack profile when generated from an involute system?