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Guide to starting a project using a kinematic chain

In mechanical projects, the study and application of a kinematic chain (gear train) is a widespread mechanism to transfer both the rotational motion and torque.

If you are facing a project that uses motion transmission mechanisms, this simple guide may help you understand the concept, get to know the types of gear trains in the chain, and the main problems that you may stumble upon.

In this post we will offer you all the information you need to start a project of this type. Pay attention!

 

What is a kinematic chain?

Kinematic chains or motion transmission mechanisms through the use of gears are systems composed of several interconnected gears , individually called “gear train stage”.

In countless machines, the transmission of rotations between shafts cannot be accomplished by using a single gear pair, so it is therefore necessary to use a combination of gears joined to one another in different manners.

These gear trains are used in wildly different machines. The main element of this mechanism is a gear with two spur gears, which is composed of two gears engaged with each other with the same module but different number of teeth.

The entire system is composed of several of these gears in a chain, where each one transmits the motion to the next. Depending on which one is chosen as the driver and which as the driven, we will obtain a function, a gear ratio or a speed increase.

 

The importance of a proper study of the gear ratio

Performing a painstaking gear kinematic study during our project’s design phase will help us achieve a stable gear ratio throughout the entire gear train.

 

 How to calculate the gear ratio between two gears

The equation that relates the angular speed with the radius is as follows:

      i=ω2/ω1=R1/R2

Here:

  • i=Gear ratio
  • R1=Pitch radius of the first gear
  • R2=Pitch radius of the second gear
  • ω1=Angular speed of the first gear
  • ω2=Angular speed of the second gear

Based on the number of teeth (z), we can define it as:

      i=ω2/ω1=Z1/Z2

Where:

  • i=Gear ratio
  • Z1=Number of teeth on the first gear
  • Z2=Number of teeth on the second gear

By using this equations, and based on the angular speed of each gear, we can calculate the relation between the number of teeth or radii and vice-versa.

You might be interested in: Gear calculations: essential ideas for your mechanical transmissions

Gear design

Types of gear trains

From a kinematic standpoint, they may be classified as per the following three types:

Ordinary gear trains

The gears located at the start and end of the kinematic chain rotate on two shafts for which a target gear ratio is to be established. All gear shafts (for both outer and inner gears) rest on the same fixed support. These types of gear trains can be subdivided into:

  • Simple ordinary gear trains: When each shaft has only one gear. All gears must have the same module. The number of teeth in inner gears do not influence the absolute value of the gear ratio (μ).
  • Compound ordinary gear trains: When at least one of the two shafts is shared by several gears.

ordinary gear train

Planetary gear trains

These are gear trains in which some wheel rotates around a shaft that is not fixed, but rotates in space. Depending on whether the input and output shafts are coaxial, they will be categorised as reverted or non-reverted. Within this classification, we can find:

  • Simple planetary gear trains.
  • Differential.
  • Rocker planetary gear trains.

planetary gear train

Combined gear trains

Combines the two types of gear trains above.

Basically, the main difference between gear train types lies in that epicyclic (planetary) gear trains have some shaft that has a relative motion in relation to the others, while in ordinary gear trains the only motion shafts may have is around themselves.

 

Problems with gear trains

A project with a kinematic chain has to be designed taking into account that certain problems may arise if calculation are incorrect. If this happens, the parts may get worn or even break, and pressure would be lost on the system.

Therefore, if we intend to start a project using gear trains, we cannot forgo of the following problems that may emerge in geared transmissions and the possible actions that can correct or minimise these issues:

  • Wear due to abrasion Caused by small, hard particles that contaminate the oil, causing scratches on the gear tooth when in contact.

Remedial actions include: Draining and flushing the residues from the oil; fully washing the internal surfaces of the gearbox; cleaning and flushing all oil ducts; fill the gearbox with thin flushing oil and unladen start-up for a few minutes; clean vents and replace seals and filters; check the environment for possible contamination; and drain the flushing oil and refill with the recommended oil.

  • Wear due to corrosion Caused by the reaction resulting from the contact with acid and metal. It is usually identified due to the appearance of stains and corrosion.

Remedial actions include: For a system overload, reduce the load or improve the system, but when the overload cannot be corrected, prevent  that extreme pressure through the use of lubricant. Likewise, it is necessary to know whether the lubricant is the wrong grade, and it would therefore be fundamental to check with the manufacturer what the proper lubricant is. If, on the contrary, the problem results from not following the maintenance recommendations, the proper procedures should be checked with the manufacturer and oil change frequency should be increased.

  • Electrical pitting This happens when an electric arc is discharged through the oil film between engaged gear teeth.

A remedial action would be to ground the same side of the bearing box when welding; add a ground connection by placing ground wires from the machine to the electric or pneumatic piping in order to reduce the static electricity created by the manufacturing process; or check that the electrical system is properly installed and grounded.

 

Electrical pitting

 

  • Rolling and indentation These problems are caused due to the gear teeth not engaging properly, and are completely damaged after use.

Rolling damage results from the deformation of the metal at the active area of the tooth caused by the high level of contact.

Indentation takes place when the surface of the tooth is uneven or misaligned.

  • Wear due to fatigue Wear caused due to repeat stress. Fatigue may be identified based on cracks or fracture:
  • Crack due to fatigue Crack on the gear that takes place due to bending, mechanical stress, thermal stress or material failure.
  • Fatigue fracture is the breakage or tear of a gear tooth.

It is worth mentioning that cracks due to fatigue usually result in a fracture when the crack grows up to a point in which the remaining section of the tooth can no longer bear the load.

 

 

  • Failure in the plastic flow Consists of a type of surface deformation caused by stress due to high contact with rolling and sliding when teeth engage. It normally takes place in gears made out of soft materials, but may happen in hardened gears when heavy loads are present.
  • Failure due to surface fatigue This is a failure that results from surface or subsurface stress on the material, overcoming the hardening limit.

Initial pitting is caused by the high stress in local areas due to the irregularity of the tooth surface.

Scaling is caused due to excessive stress due to high contact. It is similar to pitting, but pits are larger, deeper and not uniform.

  • Excessive gear wear In order to prevent excessive gear wear, it is paramount to check the HP requirement to study a possible replacement with hardened gears of the same size, or replacing with gears that have a wider face width.

Likewise, it is necessary to check that they have a proper lubrication.

  • Excessive noise on the transmission mechanisms It is vital to check that the gear set is correct; if it is not, adjust it. The transmission may also be redesigned to increase its capability and check that they have the proper lubrication.
  • Gear breakage This happens due to an overload or shock loading. In order to prevent it, it is necessary to eliminate the overload or the conditions that result in shock loading, or change the transmission using wider gears or gears that have a 20° pressure angle.

Likewise, the proper lid needs to be used in order to protect the environmental material around the transmission from contaminants that may enter the transmission.

  • Tooth warping In order to prevent this problem it is necessary to eliminate the overload or replace it with hardened gears.

By keeping in mind the problems that may emerge in projects using gear trains, we will be better prepared when undertaking an activity of this type, minimising the ill effects that may emerge that hamper our process.

At Mootio, a brand by Compañía Levantina de Reductores (CLR), we have a wide selection of materials, specific treatments and a dedication to the engineering of precision gears.

Our goal is to help any inventor or project developer in finding the most appropriate components or custom gears. This is why, when buying gears, whether gear sets, plastic gears or metal gears, Mootio helps you design the motion transmission you need. Do you have problems calculating gear ratios? Is it difficult for you to correctly calculate powers and torques transferred? How can we be of assistance?

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