Evolution and Analysis of the Toothbrush
Finite-Element Analysis and A Winning Smile
The following article on the evolution and analysis of the toothbrush was written by Kyle Sembera, a mechanical engineering senior at Lamar University, Beaumont, Tex., as a final assignment for an elective design class. Sembera’s toothy research project was inspired by course professor P.R. Corder who, during a recent visit to the dentist, found himself musing on the merits of modern toothbrush design.
Have you ever tried brushing your teeth with a smashed stick? While today there are many sophisticated options for the orally conscious, during the dawn of civilization, the smashed stick—the earliest predecessor of the modern toothbrush—had a corner on the market. By chewing the end of a soft twig flat, people created a rudimentary brush, which aided in the removal of food particles. Before this method was developed, people may have used a stick similar to a toothpick to perform the task.
Demonstrating the benefits of modern toothbrush technology ME senior Kyle Sembera flashes his pearly whites.
Because of the ubiquitous place toothbrushes hold in modern society, the need no longer exists to brush with a smashed stick, yet some native tribes still use simple sticks to clean their teeth.
This article looks at the origin and evolution of modern toothbrushing and, for those who have ever worried about catastrophic toothbrush failure, assuages fears with a finite-element analysis, comparing a traditionally styled toothbrush to a modern one.
Origin of the Toothbrush
During eighteenth-and nineteenth-century Europe, ornate metal toothpicks were developed. Serving as both art and status symbol, these were often copper, silver, or even gold.
Currently, some 10 million people in the Middle East and other parts of the world use toothpicks daily as their primary tooth-cleaning mechanism. In fact, toothpicks were used as the primary method for cleaning teeth as late as the early 1950s in some isolated sections of the United States.
Addis attached hairs from the tail of a cow to the end of a whittled thighbone from the same animal, which was reportedly the only bone strong enough to survive the bristle-attachment procedure and still maintain its strength when wet. Eventually, boar hairs replaced the hairs from the cow’s tail. To this day, descendants of William Addis still manufacture toothbrushes at a factory in England.
The nylon filament came with several advantages, including a dramatic reduction in production costs and the ability to control bristle texture. Manufacturers could also shape the filament tip and vary its diameter for improved performance. Boar hair, on the other hand, often fell out, did not dry well, and was prone to bacterial growth. Although nylon continues to dominate the market today, boar-hair bristles still account for about 10 percent of toothbrushes sold worldwide.
One manufacturer markets both a toothbrush with two heads which surround the teeth, claiming it will clean teeth more effectively, and a toothbrush with a built-in tongue scraper, designed to remove bacteria, which builds up on the tongue.
Another manufacturer stresses the importance of maintaining a cleaner toothbrush. Their design incorporates a unique hole in the center of the bristle head, ensuring that all food and other debris is easily rinsed off the brush. Still other manufacturers stress that bristle orientation is key to maintaining clean teeth. They sell toothbrushes with angled bristles, which tackle the teeth at different angles to maximize cleaning effectiveness.
One thing most manufacturers can agree on is the importance of having a handle that assists the user in reaching the back teeth, the most neglected and difficult to reach. One popular remedy has been to angle the toothbrush handle.
Figure 1-Classic-Style Toothbrush
Comparison Between an Old-Style and a Modern Toothbrush
Figure 2-Modern Style Toothbrush
In contrast, the modern toothbrush has a larger cross-section as well as a reinforced handle where the higher stresses are expected (Figure 2). The gently angled section at the head of the brush absorbs the majority of the brushing load and prevents a large stress concentration. The increased cross-sectional thickness allows the brush to withstand a greater load with less deflection. In order to compare stress within the brush and the overall deflection of the toothbrush’s tip, each toothbrush bristle area was loaded with 35 N (approximately 8 lbs.) distributed uniformly on the head of the brush. Each material was assumed to be common plastic (PVC), with yield strength of 17 MPa. This load is rather large (about twice what one might expect), but it does give a reasonable comparison between the two brushes.
Each brush was constrained at the point where the hand would grip, which is also where the cross-sectional geometries of the brushes change significantly.
Figure 3- Classic-Style Toothbrush dimensions, load application, and high stress point.
The classic brush experiences most of its stress at two significant area changes: where the handle narrows to meet the neck, and again where the neck meets the brush head. The larger stress occurs at the latter point, where the neck is only 8mm wide (Figure 3). The Von Mises stress in this brush peaks at about 7.8 N/mm squared (1,131 psi) in this section, while the brush tip deflects 8.6 mm over this length of the tip (about 66 mm or 13 percent deflection).
Figure 4 illustrates the modern brush with the same 35 N load applied. It has only one major stress concentration: where the neck of the brush meets the head. The Von Mises stress at this point reaches only 3.6 N/mm squared, or 522 psi (roughly half that of the classic brush).
Figure 4-This view shows the major stress concentration where the neck meets the head, caused by the change in geometry.
The larger cross-section and less abrupt changes in geometry (sloped versus the flat neck) help reduce the amount of stress in this brush. However, the largest difference between these two brushes is portrayed in their maximum displacement difference. The modern toothbrush deflects 1.6 mm over its length of 73 mm, just over 2 percent deflection, compared to the classic brush’s 13 percent.
The 35 N loads were rather large, yet the deflections and stresses exhibited by these brushes should not affect the brush’s performance over its relatively short lifetime. Neither brush would be expected to fail due to these loads, because the stresses are found to be significantly lower than the yield strength of the material (7.8 and 3.6 MPa vs. a yield strength of 17 MPa).
Over the centuries, the toothbrush has seen many changes in configuration, material and geometry. Today’s toothbrushes come in a large variety of shapes, styles, sizes, and colors, yet despite this incredible selection, toothbrush geometry is not nearly as important to dental health as brushing frequency and technique. All of today’s brushes should be able to withstand any reasonable brushing load; therefore, the brush that suits you best is the one you enjoy using.
Toothpaste has a history that stretches back nearly 4,000 years. Until the mid-nineteenth century, abrasives used to clean teeth did not resemble modern toothpastes. People were primarily concerned with cleaning stains from their teeth and used harsh, sometimes toxic ingredients to meet that goal. Ancient Egyptians used a mixture of green lead, verdigris (the green crust that forms on certain metals like copper or brass when exposed to salt water or air), and incense. Ground fish bones were used by the early Chinese.
In the Middle Ages, fine sand and pumice were the primary ingredients in teeth-cleaning formulas used by Arabs. Arabs realized that using such harsh abrasives harmed the enamel of the teeth. Concurrently, however, Europeans used strong acids to lift stains. In western cultures, similarly corrosive mixtures were widely used until the twentieth century. Table salt was also used to clean teeth.
In 1850, Dr. Washington Wentworth Sheffield, a dental surgeon and chemist, invented the first toothpaste. He was 23 years old and lived in New London, Connecticut. Dr. Sheffield had been using his invention, which he called Creme Dentifrice, in his private practice. The positive response of his patients encouraged him to market the paste. He constructed a laboratory to improve his invention and a small factory to manufacture it.
Modern toothpaste was invented to aid in the removal foreign particles and food substances, as well as clean the teeth. When originally marketed to consumers, toothpaste was packaged in jars. Chalk was commonly used as the abrasive in the early part of the twentieth century.
Sheffield Labs claims it was the first company to put toothpaste in tubes. Washington Wentworth Sheffield's son, Lucius, studied in Paris, France, in the late nineteenth century. Lucius noticed the collapsible metal tubes being used for paints. He thought putting the jar-packaged dentifrice in these tubes would be a good idea. Needless to say, it was adopted for toothpaste, as well as other pharmaceutical uses. The Colgate-Palmolive Company also asserts that it sold the first toothpaste in a collapsible tube in 1896. The product was called Colgate Ribbon Dental Creme. In 1934, in the United States, toothpaste standards were developed by the American Dental Association's Council on Dental Therapeutics. They rated products on the following scale: Accepted, Unaccepted, or Provisionally Accepted.
The next big milestone in toothpaste development happened in the mid-twentieth century (1940-60, depending on source). After studies proving fluoride aided in protection from tooth decay, many toothpastes were reformulated to include sodium fluoride. Fluoride's effectiveness was not universally accepted. Some consumers wanted fluoride-free toothpaste, as well as artificial sweetener-free toothpaste. The most commonly used artificial sweetener is saccharin. The amount of saccharin used in toothpaste is minuscule. Companies like Tom's of Maine responded to this demand by manufacturing both fluoridated and non-fluoridated toothpastes, and toothpastes without artificial sweetening.
Many of the innovations in toothpaste after the fluoride breakthrough involved the addition of ingredients with "special" abilities to toothpastes and toothpaste packaging. In the 1980s, tartar control became the buzz word in the dentifrice industry. Tarter control toothpastes claimed they could control tartar build-up around teeth. In the 1990s, toothpaste for sensitive teeth was introduced. Bicarbonate of soda and other ingredients were also added in the 1990s with claims of aiding in tartar removal and promoting healthy gums. Some of these benefits have been largely debated and have not been officially corroborated.
Packaging toothpaste in pumps and stand-up tubes was introduced during the 1980s and marketed as a neater alternative to the collapsible tube. In 1984, the Colgate pump was introduced nationally, and in the 1990s, stand-up tubes spread throughout the industry, though the collapsible tubes are still available.
Every toothpaste contains the following ingredients: binders, abrasives, sudsers, humectants, flavors (unique additives), sweeteners, fluorides, tooth whiteners, a preservative, and water. Binders thicken toothpastes. They prevent separation of the solid and liquid components, especially during storage. They also affect the speed and volume of foam production, the rate of flavor release and product dispersal, the appearance of the toothpaste ribbon on the toothbrush, and the rinsibility from the toothbrush. Some binders are karaya gum, bentonite, sodium alginate, methylcellulose, carrageenan, and magnesium aluminum silicate.
Abrasives scrub the outside of the teeth to get rid of plaque and loosen particles on teeth. Abrasives also contribute to the degree of opacity of the paste or gel. Abrasives may affect the paste's consistency, cost, and taste. Some abrasives are more
harsh than others, sometimes resulting in unnecessary damage to the tooth enamel.
The most commonly used abrasives are hydrated silica (softened silica), calcium carbonate (also known as chalk), and sodium bicarbonate (baking soda). Other abrasives include dibasic calcium phosphate, calcium sulfate, tricalcium phosphate, and sodium metaphosphate hydrated alumina. Each abrasive also has slightly different cleaning properties, and a combination of them might be used in the final product.
Sudsers, also known as foaming agents, are surfactants. They lower the surface tension of water so that bubbles are formed. Multiple bubbles together make foam. Sudsers help in removing particles from teeth. Sudsers are usually a combination of an organic alcohol or a fatty acid with an alkali metal. Common sudsers are sodium lauryl sulfate, sodium lauryl sulfoacetate, dioctyl sodium sulfosuccinate, sulfolaurate, sodium lauryl sarcosinate, sodium stearyl fumarate, and sodium stearyl lactate.
Humectants retain water to maintain the paste in toothpaste. Humectants keep the solid and liquid phases of toothpaste together. They also can add a coolness and/or sweetness to the toothpaste; this makes toothpaste feel pleasant in the mouth when used. Most toothpastes use sorbitol or glycerin as humectants. Propylene glycol can also be used as a humecant.
Toothpastes have flavors to make them more palatable. Mint is the most common flavor used because it imparts a feeling of freshness. This feeling of freshness is the result of long term conditioning by the toothpaste industry. The American public associates mint with freshness. There may be a basis for this in fact; mint flavors contain oils that volatize in the mouth's warm environment. This volatizing action imparts a cooling sensation in the mouth. The most common toothpaste flavors are spearmint, peppermint, wintergreen, and cinnamon. Some of the more exotic toothpaste flavors include bourbon, rye, anise, clove, caraway, coriander, eucalyptus, nutmeg, and thyme.
In addition to flavors, toothpastes contain sweeteners to make it pleasant to the palate because of humecants. The most commonly used humectants (sorbitol and glycerin) have a sweetness level about 60% of table sugar. They require an artificial flavor to make the toothpaste palatable. Saccharin is the most common sweetener used, though some toothpastes contain ammoniated diglyzzherizins and/or aspartame.
Fluorides reduce decay by increasing the strength of teeth. Sodium fluoride is the most commonly used fluoride. Sodium perborate is used as a tooth whitening ingredient. Most toothpastes contain the preservative p-hydrozybenzoate. Water is also used for dilution purposes.
1 After transporting the raw materials into the factory, the ingredients are both manually and mechanically weighed. This ensures accuracy in the ingredients' proportions. Then the ingredients are mixed together. Usually, the glycerin-water mixture is done first.
2 All the ingredients are mixed together in the mixing vat. The temperature and humidity of vat are watched closely. This is important to ensuring that the mix comes together correctly. A commonly used vat in the toothpaste industry mixes a batch that is the equivalent of 10,000 four-ounce (118 ml) tubes.
3 Before tubes are filled with toothpaste, the tube itself passes under a blower and a vacuum to ensure cleanliness. Dust and particles are blown out in this step. The tube is capped, and the opposite end is opened so the filling machine can load the paste.
4 After the ingredients are mixed together, the tubes are filled by the filling machine. To make sure the tube is aligned correctly, an optical device rotates the tube. Then the tube is filled by a descending pump. After it is filled, the end is sealed (or crimped) closed. The tube also gets a code stamped on it indicating where and when it was manufactured.
5 After tubes are filled, they are inserted into open paperboard boxes. Some companies do this by hand.
6 The boxes are cased and shipped to warehouses and stores.
Each batch of ingredients is tested for quality as it is brought into the factory. The testing lab also checks samples of final product.