Unidad 10 -Engranajes - Interferencia parte 1

Interference in Gear Profiles

Introduction to Gear Profiles

• The discussion begins with an overview of involute gear profiles, which are the most commonly used in practice.

• It introduces the concept of interference, a phenomenon specific to involute profiles that needs thorough understanding and evaluation.

Types of Interference

• Two types of interference are identified: mechanical interference and geometric interference. The focus will be on explaining each type in detail.

Mechanical Interference

• Mechanical interference typically occurs in gears with fewer than 30 to 40 teeth or those with low pressure angles.

• This issue arises when the inner diameter of a gear is smaller than its base diameter, indicating a lack of proper involute profile generation.

Profile Generation Issues

• If the inner diameter is below the base diameter, there will be no involute profile generated from that point inward.

• As teeth count decreases while maintaining constant module and pressure angle, the primitive diameter also reduces but at different rates leading to potential interference.

Critical Parameters for Interference

• The minimum number of teeth (Z_min) where mechanical interference appears depends on the pressure angle; for example:

• At 15 degrees: Z < 68 teeth

• At 20 degrees: Z < 38 teeth

• At 22 degrees: Z < 30 teeth

Examples and Calculations

• An example illustrates how varying tooth counts affect diameters:

• A gear with a module of three and a pressure angle of 20 degrees has no interference if it has more than 50 teeth.

• Conversely, reducing this to a gear with only 30 teeth results in mechanical interference due to dimensional discrepancies.

Consequences of Mechanical Interference

• When gears with mechanical interference are manufactured using generating systems, they can develop undercuts between their base and inner diameters since no involute can be formed below the base.

Undercutting Phenomenon

• The resulting undercutting creates a non-involute profile beneath the base diameter, leading to performance issues.

Manufacturing Systems Impacting Interference

• Different manufacturing systems produce varying levels of undercutting based on tool design:

• Tools designed for infinite tooth counts create maximum undercutting.

• Finite-tooth tools result in less severe undercutting effects.

Summary on Tool Design Effects

• The extent of undercutting varies inversely with the number of teeth on the cutting tool; fewer teeth lead to lesser undercuts compared to tools designed for infinite tooth counts.

Understanding Mechanical Interference in Gear Systems

Maximum Possible Undercut

• The maximum possible undercut is achieved when a pinion works with a gear that has an infinite number of teeth, ensuring no contact with the undercut area.

• If the gear produced has a finite number of teeth, it may lead to a smaller undercut, potentially causing interference if paired with another gear having fewer teeth than the cutter.

Mechanical Interference Effects

• A mechanical interference can occur when the number of teeth on the engaging gears differs significantly; this could lead to potential jamming at the tooth head.

• However, this interference does not severely affect the active flank since it originates from the base diameter and primarily weakens the tooth root under load.

Impact on Tooth Resistance

• While mechanical interference reduces tooth resistance due to undercutting at the base, its impact is considered manageable as it does not compromise critical sections of the tooth.

• Visual aids are provided to illustrate how different positions during generation affect profile creation and highlight areas where material has been removed.

Geometric Interference Explained

• Geometric interference occurs when part of a gear segment extends beyond defined tangential limits, leading to real contact points outside these boundaries.

• The segment of engagement is defined by all real contact points between active flanks and gears; any deviation indicates geometric interference.

Analyzing Contact Points

• In analyzing two gears where one drives another, normals are drawn at tangential points (A and B), which define ideal contact conditions for proper operation.

• As one wheel rotates through various enveloping positions, multiple real contact points (n1, n2, n3) remain within tangential limits without causing geometric interference.

Consequences of Geometric Interference

• When real contact points exceed tangential limits (e.g., point n4), they disrupt normal operations as profiles no longer maintain necessary tangency.

• This results in non-compliance with general gearing laws; thus, geometric interferences reduce effective engagement and alter performance dynamics.

Conditions for Analysis

• The analysis involves two gears working without mechanical or geometric interference while maintaining constant center distance and pressure angle throughout their operation.

• Adjustments in parameters such as tooth count influence module size and overall dimensions affecting performance characteristics.

Mechanical Interference in Gear Systems

Understanding Diameter Modifications

• The modification of external diameters is discussed, indicating that an increase in the module leads to an increase in the outer diameter.

• As the number of teeth (Z1 and Z2) decreases while increasing the module, it results in a decrease of inner diameters for wheels 1 and 2.

Analyzing Mechanical Interference

• A graphical representation is introduced to illustrate how mechanical interference occurs as contact points between flanks f1 and f2 are established.

• The importance of maintaining constant primitive diameters while increasing the module is emphasized; this affects tooth height and consequently alters gear dimensions.

Graphical Representation of Gear Changes

• Only increases in outer diameter for gears with more teeth and decreases in inner diameter for those with fewer teeth are graphically represented.

• The presence of undercutting due to decreased inner diameter leading to mechanical interference is highlighted.

Conditions Leading to Interference

• Increasing the module raises both outer diameter and tooth height, affecting gear engagement points significantly.

• Contact points shift as modifications occur, which can lead to increased undercutting without affecting active flank geometry.

Minimum Teeth Count for Avoiding Geometric Interference

• A discussion on maintaining constant primitive diameters while reducing tooth count reveals potential geometric interferences at lower counts.

• The segment defined by new contact points indicates a risk of escaping tangential limits, necessitating adjustments to avoid interference.

Mathematical Study on Tooth Count

• It’s proposed that there exists a minimum number of teeth where geometric interference begins; further reductions lead to significant issues.

• A triangle formation using key tangential limit points helps visualize conditions leading up to geometric interferences.

Conclusion on Gear Design Considerations

• The necessity of understanding these dynamics is crucial for effective gear design; avoiding geometric interference should be prioritized.

• Using previous graphs, mathematical determination aims at identifying critical thresholds for tooth counts before encountering issues.

Understanding Gear Interference and Minimum Teeth Calculation

Application of Pythagorean Theorem in Gears

• The relationship between the hypotenuse and the sides of a triangle formed by gear components is established using the Pythagorean theorem, where the square of the hypotenuse equals the sum of the squares of both catheti.

• Variables are defined: rb1 represents the radius of the wheel, while m and MB denote primitive radii related to different gear types, specifically for sine calculations involving angles.

Determining Minimum Teeth on Pinion

• A second-degree equation emerges from mathematical manipulation aimed at determining the minimum number of teeth (zp) required on a pinion to avoid geometric interference with a given wheel's teeth count.

• The minimum pinion teeth count is influenced by factors such as wheel tooth count and pressure angle, indicating that these variables must be controlled to maintain proper function without interference.

Influence of Pressure Angle on Gear Design

• As pressure angle increases, it allows for fewer teeth on the pinion without causing interference; specific examples show how varying angles yield different minimum tooth counts (e.g., 30 teeth for 15 degrees).

• A practical minimum (zp práctico) is introduced as being approximately five-sixths of theoretical values due to tool radius considerations during manufacturing processes. This distinction helps clarify design parameters.

Graphical Representation and Hypothetical Scenarios

• A graphical representation illustrates how variations in wheel tooth count affect pinion design; this includes hypothetical scenarios where certain conditions lead to non-applicable results but provide insight into theoretical limits.

• The graph shows a curve representing changes in minimum pinion teeth based on wheel tooth count, emphasizing practical applications versus theoretical constructs in gear design.

Methods for Reducing Geometric Interference

• Three methods are proposed to eliminate or reduce geometric interferences in gears, focusing primarily on achieving complete elimination rather than just mitigation; secondary goals include minimizing mechanical interferences that could weaken gear integrity.

• Emphasis is placed on understanding how gears manufactured through generation processes can achieve optimal performance with any number of teeth while maintaining structural integrity against potential interferences.

Adjusting Pressure Angles for Improved Performance

• Increasing pressure angles can effectively reduce potential geometric interferences by altering base diameters; this adjustment leads to improved compatibility among gear profiles under various operational conditions.

• Visual aids demonstrate how changing pressure angles impacts mechanical interference levels within gears, showcasing practical implications for engineering designs focused on efficiency and reliability.

Understanding Gear Mechanics and Pressure Angles

The Impact of Base Diameter on Gears

• The pressure in the pinion affects the transition from Alpha to Alpha prime, influencing the primitive diameters of both wheel and pinion.

• A constant outer diameter leads to a decrease in the base diameter of the pinion, which subsequently reduces its effectiveness.

Changes in Gear Segment Length with Pressure Angle

• Introduction of a new gear normal that alters inclination with a larger segment; this results in shorter gear segments for higher pressure angles.

• As the pressure angle increases, both the gear segment length and arc size diminish, leading to increased noise within mechanisms.

Geometric Interference and Tangential Limits

• Modifying base diameters establishes new tangential limits (A prime B prime), which can help eliminate geometric interferences if they exist.

• If geometric interferences were present when transitioning from point B to B prime, it could lower tangential limits and recover points outside these limits.

Advantages and Disadvantages of Increased Pressure Angles

• Increasing pressure angles can reduce or eliminate geometric interferences while enhancing robustness at the base of teeth due to wider profiles.

• However, increasing angle Alpha raises radial force components on teeth, making them sharper at tips; caution is needed to avoid cutting off tips during manufacturing.

Limitations in Application

• This method cannot be applied universally as modifications may dilute performance; specifically, it cannot be used on pre-manufactured wheels without altering their design.